Download App

Maths M.C.Q

Lines And Angles [NEW] · Gujarat Board (GSEB) STD 9 (GSEB - English Medium). 45 questions.

Questions

M.C.Q

🎯

Test yourself on this topic

45 questions · timed · auto-graded

MCQ 11 Mark
Two straight lines AB and CD intersect one another at the point O. If $\angle A O C+\angle C O B+\angle B O D=274^{\circ}$, then $\angle A O D=$
  • ✓
    $80^{\circ}$
  • B
    $90^{\circ}$
  • C
    $94^{\circ}$
  • D
    $137^{\circ}$
Answer
Correct option: A.
$80^{\circ}$
a
View full question & answer→
MCQ 21 Mark
Two straight lines AB and CD cut each other at O. If $\angle B O D=63^{\circ}$, then $\angle B O C=$
  • A
    $63^{\circ}$
  • ✓
    $117^{\circ}$
  • C
    $17^{\circ}$
  • D
    $153^{\circ}$
Answer
Correct option: B.
$117^{\circ}$
b
View full question & answer→
MCQ 31 Mark
Two lines AB and CD intersect at O. If $\angle A O C+\angle C O B+\angle B O D=270^{\circ}$, then $\angle A O C=$
  • A
    $70^{\circ}$
  • B
    $80^{\circ}$
  • ✓
    $90^{\circ}$
  • D
    $180^{\circ}$
Answer
Correct option: C.
$90^{\circ}$
c
View full question & answer→
MCQ 41 Mark
Two complementary angles are such that two times the measure of one is equal to three times the measure of the other. The measure of the smaller angle, is
  • A
    $45^{\circ}$
  • B
    $30^{\circ}$
  • ✓
    $36^{\circ}$
  • D
    none of these
Answer
Correct option: C.
$36^{\circ}$
c
View full question & answer→
MCQ 51 Mark
Two angles are supplementary. One of them is an acute angle. Which of the following could be the measure of the other angle?
  • A
    $60^{\circ}$
  • B
    $120^{\circ}$
  • C
    $200^{\circ}$
  • D
    $240^{\circ}$
Answer
B. $120^{\circ}$
Let $x$ and $y$ be the degree measures of two supplementary angles such that $x$ is an acute angle i.e. $x<90^{\circ}$. Then
 $x+y=180^{\circ}$ $\Rightarrow y=180^{\circ}-x$ $\Rightarrow$ $90^{\circ}$ < y < $180^{\circ}$ 
 Clearly, option (b) satisfies this relation.
View full question & answer→
MCQ 61 Mark
The measure of an angle which is twice its supplement is
  • A
    $60^{\circ}$
  • B
    $120^{\circ}$
  • C
    $110^{\circ}$
  • D
    $130^{\circ}$
Answer
B. $120^{\circ}$
Let the measure of the required angle be $x^{\circ}$. Then the measure of its supplement is $180^{\circ}-x^{\circ}$. It is given that
$
x=2(180-x) \Rightarrow 3 x=360 \Rightarrow x=120
$
View full question & answer→
MCQ 71 Mark
The measure of an angle which excends its complement by $30^{\circ}$ is
  • A
    $150^{\circ}$
  • B
    $120^{\circ}$
  • C
    $60^{\circ}$
  • D
    $80^{\circ}$
Answer
C. $60^{\circ}$
 Let the measure of the required angle be $x^{\circ}$. Then, the measure of its complement is $90^{\circ}-x^{\circ}$. It is given that
$
x-(90-x)=30 \Rightarrow 2 x=120 \Rightarrow x=60
$
View full question & answer→
MCQ 81 Mark
One angle is equal to three times its supplement. The measure of the angle is
  • A
    $130^{\circ}$
  • ✓
    $135^{\circ}$
  • C
    $90^{\circ}$
  • D
    $120^{\circ}$
Answer
Correct option: B.
$135^{\circ}$
b
View full question & answer→
MCQ 91 Mark
In Fig. which of the following statements must be true?
(i) a+b=d+c$\quad$(ii) $a+c+e=180^{\circ}$$\quad$(iii) b+f=c+e
Image
  • A
    (i) only
  • B
    (ii) only
  • C
    (iii) only
  • ✓
    (ii) and (iii) only
Answer
Correct option: D.
(ii) and (iii) only
d
View full question & answer→
Question 101 Mark
In Fig , two parallel lines $l$ and $m$ are intersected by a transversal $n$. Which one of the following statements is correct?

(a) $c+e=180^{\circ}$ as $c$ and $e$ are alternate interior angles.
(b) $d=h$ as $d$ and $h$ are corresponding angles.
(c) $b=g$ as $b$ and $g$ are corresponding angles.
(d) $a=e$ as $a$ and $e$ are alternate interior angles.
Image
Answer
B. $d=h$ as $d$ and $h$ are corresponding angles.
We observe that $c=e$ as these are alternate angles. So, statement (a) is not correct. We find that $d$ and $h$ are corresponding angles. Therefore, $d=h$. So, statement (b) is correct.
Statement (c) is not correct as $b$ and $g$ are not corresponding angles.
Finally, we find that $a$ and $e$ are corresponding angles. Therefore $a=e$. So, statement (d) is not correct.
View full question & answer→
Question 111 Mark
In Fig , two lines $A B$ and $C D$ are cut by a transversal $P Q$. Is it true that lines $A B$ and CD are parallel?

(a) Yes, because measures of corresponding angles $\angle D R S$ and $\angle B S P$ are equal and their measure is $130^{\circ}$.
(b) No, because $\angle D R S=155^{\circ}$ and $\angle B S P=160^{\circ}$, which indicates that corresponding angles are not equal.
(c) No, because $\angle D R S=130^{\circ}$ and $\angle B S P=150^{\circ}$, which indicates that corresponding angles are not equal.
(d) Yes, because measures of alternate angles $\angle B S P$ and $\angle D R S$ are equal and their measures is $130^{\circ}$.
Image
Answer
A. Yes, because measures of corresponding angles $\angle D R S$ and $\angle B S P$ are equal and their measure is $130^{\circ}$.
We find that $\angle B S P$ and $\angle A S P$ form a linear pair.$
\begin{array}{ll}
\therefore & \angle B S P+\angle A S P=180^{\circ} \Rightarrow 5 x+5+2 x=180 \Rightarrow 7 x=175 \Rightarrow x=25 \\
\therefore & \angle B S P=(5 \times 25+5)^{\circ}=130^{\circ} \text { and } \angle D R S=(6 \times 25-20)^{\circ}=130^{\circ} \\
\Rightarrow & \angle B S P=\angle D R S
\end{array}
$
Thus, lines $A B$ and $C D$ are intersected by transversal $P Q$ such that corresponding angles are equal. Hence, $A B \| C D$.
View full question & answer→
MCQ 121 Mark
In Fig. the value of y, is
Image
  • A
    $20^{\circ}$
  • ✓
    $30^{\circ}$
  • C
    $45^{\circ}$
  • D
    $60^{\circ}$
Answer
Correct option: B.
$30^{\circ}$
b
View full question & answer→
MCQ 131 Mark
In Fig , the value of $y$ is
Image
  • A
    36
  • B
    54
  • C
    63
  • D
    72
Answer
B. 54
Since $A O B$ is a straight line.$
\begin{array}{ll}
\therefore & \angle A O C+\angle C O D+\angle D O B=180^{\circ} \text { and } \angle A O E+\angle E O B=180^{\circ} \\
\Rightarrow & x+90+y=180 \text { and } 3 x+72=180 \\
\Rightarrow & x+y=90 \text { and } x=36 \Rightarrow x=36 \text { and } y=54
\end{array}
$
View full question & answer→
MCQ 151 Mark
In Fig. PQ ||RS, $\angle A E F=95^{\circ}, \angle B H S=110^{\circ}$ and $\angle A B C=x^{\circ}$.Then the value of x is
Image
  • A
    $15^{\circ}$
  • ✓
    $25^{\circ}$
  • C
    $70^{\circ}$
  • D
    $35^{\circ}$
Answer
Correct option: B.
$25^{\circ}$
b
View full question & answer→
MCQ 161 Mark
In Fig , POQ is a line. The value of $x$ is
Image
  • A
    $20^{\circ}$
  • B
    $25^{\circ}$
  • C
    $30^{\circ}$
  • D
    $35^{\circ}$
Answer
A. $20^{\circ}$
It is given that $P O Q$ is a straight line.
$
\begin{array}{ll}
\therefore & \angle P O S+\angle S O R+\angle R O Q=180^{\circ} \\
\Rightarrow & 40^{\circ}+4 x+3 x=180^{\circ} \Rightarrow 7 x=140^{\circ} \Rightarrow x=20^{\circ}
\end{array}
$
View full question & answer→
MCQ 171 Mark
In Fig , if transversal $A B$ cuts parallel lines $P Q$ and $R S$ at $L$ and $M$ respectively. Then, then the value of $x$ is
Image
  • A
    $20^{\circ}$
  • B
    $24^{\circ}$
  • C
    $30^{\circ}$
  • D
    $34^{\circ}$
Answer
B. $24^{\circ}$
We find that $\angle Q L M$ and $\angle S M L$ are alternate interior angles.$
\therefore \quad 4 x+12+2 x+24=180^{\circ} \Rightarrow 6 x+36^{\circ}=180^{\circ} \Rightarrow 6 x=144^{\circ} \Rightarrow x=24^{\circ}
$
View full question & answer→
MCQ 181 Mark
In Fig , if $O P \| R S, \angle O P Q=100^{\circ}$ and $\angle Q R S=130^{\circ}$, then $\angle P Q R$ is equal to
Image
  • A
    $40^{\circ}$
  • B
    $50^{\circ}$
  • C
    $60^{\circ}$
  • D
    $70^{\circ}$
Answer
C. $60^{\circ}$
Through $Q$, draw $A Q B\|O P\| R S$.
Now, $O P \| A B$ and transversal $P Q$ cuts them at $P$ and $Q$ respectively.
$\therefore$ $\angle O P Q+\angle A Q P=180^{\circ}$
$\Rightarrow$ $110^{\circ}+\angle A Q P=180^{\circ}$
$\Rightarrow$ $\angle A Q P=70^{\circ}$
$A B \| R S$ and transversal $Q R$ cuts them at $Q$ and $R$ respectively.
$\therefore$ $\angle B Q R+\angle Q R S=180^{\circ} \Rightarrow \angle B Q R+130^{\circ}=180^{\circ} \Rightarrow \angle B Q R=50^{\circ}$
Since, AQB is a straight line. Therefore,
$\angle A P Q+\angle B Q R+\angle P Q R=180^{\circ}$ $\Rightarrow 70^{\circ}+50^{\circ}+\angle P Q R=180^{\circ}$ $\Rightarrow \angle P Q R=60^{\circ}$
View full question & answer→
MCQ 201 Mark
In Fig. if l ||m 1 then x =
Image
  • ✓
    $105^{\circ}$
  • B
    $65^{\circ}$
  • C
    $40^{\circ}$
  • D
    $25^{\circ}$
Answer
Correct option: A.
$105^{\circ}$
a
View full question & answer→
MCQ 211 Mark
In Fig. if lines I and m are parallel lines, then x =
Image
  • A
    $70^{\circ}$
  • B
    $100^{\circ}$
  • ✓
    $40^{\circ}$
  • D
    $30^{\circ}$
Answer
Correct option: C.
$40^{\circ}$
c
View full question & answer→
MCQ 221 Mark
In Fig. if line segment AB is parallel to the line segment CD, what is the value of y?
Image
  • A
    12
  • B
    15
  • C
    18
  • ✓
    20
Answer
Correct option: D.
20
d
View full question & answer→
MCQ 231 Mark
In Fig. if lines / and I are parallel, then x =
Image
  • A
    $20^{\circ}$
  • ✓
    $45^{\circ}$
  • C
    $65^{\circ}$
  • D
    $85^{\circ}$
Answer
Correct option: B.
$45^{\circ}$
b
View full question & answer→
MCQ 241 Mark
In Fig. if lines 1 and m are parallel, then the value of x is
Image
  • ✓
    $35^{\circ}$
  • B
    $55^{\circ}$
  • C
    $65^{\circ}$
  • D
    $75^{\circ}$
Answer
Correct option: A.
$35^{\circ}$
a
View full question & answer→
MCQ 251 Mark
In Fig. if $l_1 \| l_2$, what is x + y in terms of w and z?
Image
  • ✓
    180 - w + z
  • B
    180 + w - z
  • C
    180 - w - z
  • D
    180 + w + z
Answer
Correct option: A.
180 - w + z
a
View full question & answer→
MCQ 271 Mark
In Fig. if $l_1 \| l_2$, what is the value of x?
Image
  • A
    $90^{\circ}$
  • ✓
    $85^{\circ}$
  • C
    $75^{\circ}$
  • D
    $70^{\circ}$
Answer
Correct option: B.
$85^{\circ}$
b
View full question & answer→
MCQ 281 Mark
In Fig. if $l_1 \| l_2$ and $l_3 \| l_4$ what is y in terms of x?
Image
  • A
    90 + x
  • B
    90 + 2x
  • ✓
    $90-\frac{x}{2}$
  • D
    90 - 2x
Answer
Correct option: C.
$90-\frac{x}{2}$
c
View full question & answer→
MCQ 291 Mark
In Fig. if $\frac{y}{x}=5$ and $\frac{z}{x}=4$, then the value of x is
Image
  • A
    $8^{\circ}$
  • ✓
    $18^{\circ}$
  • C
    $12^{\circ}$
  • D
    $15^{\circ}$
Answer
Correct option: B.
$18^{\circ}$
b
View full question & answer→
MCQ 301 Mark
In Fig. if CP ||BQ, then the measure of x is
Image
  • ✓
    $130^{\circ}$
  • B
    $105^{\circ}$
  • C
    $175^{\circ}$
  • D
    $125^{\circ}$
Answer
Correct option: A.
$130^{\circ}$
a
View full question & answer→
MCQ 311 Mark
In Fig. if AB || HF and DE || FG, then the measure of $\angle F D E$ is
Image
  • A
    $108^{\circ}$
  • ✓
    $80^{\circ}$
  • C
    $100^{\circ}$
  • D
    $90^{\circ}$
Answer
Correct option: B.
$80^{\circ}$
b
View full question & answer→
MCQ 321 Mark
In Fig. if AB ||CD, then x =
Image
  • ✓
    $100^{\circ}$
  • B
    $105^{\circ}$
  • C
    $110^{\circ}$
  • D
    $115^{\circ}$
Answer
Correct option: A.
$100^{\circ}$
a
View full question & answer→
MCQ 331 Mark
In Fig. if AB ||CD, then the value of x is
Image
  • A
    $20^{\circ}$
  • ✓
    $30^{\circ}$
  • C
    $45^{\circ}$
  • D
    $60^{\circ}$
Answer
Correct option: B.
$30^{\circ}$
b
View full question & answer→
MCQ 341 Mark
In Fig , if $A B \| C D$, then $\angle P R Q=$
Image
  • A
    $85^{\circ}$
  • B
    $145^{\circ}$
  • C
    $135^{\circ}$
  • D
    $40^{\circ}$
Answer
A. $85^{\circ}$
Through point $R$ draw $E F\|A B\| C D$.$
\begin{array}{lll}
& \angle A P R=\angle P R F & \text { [Alternate angles] } \\
\Rightarrow & \angle P R F=180^{\circ}-135^{\circ}=45^{\circ} & \\
\text { Also, } & \angle F R Q=\angle CQR & \text { [Alternate angles] } \\
\Rightarrow & \angle F R Q=40^{\circ} &
\end{array}
$
$
\text { Hence, } \angle P R Q=\angle P R F+\angle F R Q=45^{\circ}+40^{\circ}=85^{\circ}
$
View full question & answer→
MCQ 351 Mark
In Fig , if $A B\|C D\| E F, P Q \| R S, \angle R Q D=25^{\circ}$ and $\angle C Q P=60^{\circ}$, then $\angle Q R S$ is equal to
Image
  • A
    $85^{\circ}$
  • B
    $135^{\circ}$
  • C
    $145^{\circ}$
  • D
    $110^{\circ}$
Answer
C. $145^{\circ}$
Produce $P Q$ and $S R$ to intersect $A B$ and $E F$ respectively at $L$ and $M$.
Now, $A B \| C D$ and transversal $Q R$ cuts them at $R$ and $S$ respectively.
$
\therefore \quad \angle I=25^{\circ}
$
Again, $A B \| C D$ and transversal $Q L$ cuts them at $L$ and $Q$ respectively.$
\begin{array}{lr}
\therefore & \angle 2=60^{\circ} \\
\text { But, } & \angle 2+\angle 3=180^{\circ} \\
\therefore & \angle 3=120^{\circ}
\end{array}
$
But, $\angle A R S=\angle 3$

$
\therefore \quad \angle A R S=120^{\circ}
$
But, $\angle Q R S=\angle 1+\angle A R S$

$
\therefore \quad \angle Q R S=25^{\circ}+120^{\circ}=145^{\circ}
$

View full question & answer→
MCQ 361 Mark
In Fig , if $A B, C D$ and $E F$ are three lines concurrent at $O$, then $y=$
Image
  • A
    $10^{\circ}$
  • B
    $30^{\circ}$
  • C
    $20^{\circ}$
  • D
    $15^{\circ}$
Answer
C. $20^{\circ}$
We find that $\angle A O E$ and $B O F$ are vertically opposite angles.$
\angle A O E=\angle B O F \Rightarrow \angle A O E=5 y .
$
Since $C O D$ is a straight line. Therefore,
$
\begin{array}{ll}
& \angle C O E+\angle E O A+\angle A O D=180^{\circ} \\
\Rightarrow \quad & 2 y+5 y+2 y=180^{\circ} \Rightarrow 9 y=180^{\circ} \Rightarrow y=20^{\circ}
\end{array}
$
View full question & answer→
MCQ 371 Mark
In Fig , $A O B$ is a straight line. If $x: y: z=4: 5: 6$, then $y=$
Image
  • A
    60
  • B
    80
  • C
    48
  • D
    72
Answer
A. 60
It is given that $x: y: z=4: 5: 6$.
So, let $x=4 k, y=5 k, z=6 k$. $A O B$ is a straight line.$
\begin{array}{ll}
\therefore & \angle A O C+\angle C O D+\angle D O B=180^{\circ} \\
\Rightarrow & x+y+z=180 \Rightarrow 4 k+5 k+6 k=180 \Rightarrow 15 k=180 \Rightarrow k=12 \\
\therefore & y=5 k=60
\end{array}
$
View full question & answer→
MCQ 381 Mark
In Fig. AOB is a straight line. If $\angle A O C+\angle B O D=85^{\circ}$, then $\angle C O D=$
Image
  • A
    $85^{\circ}$
  • B
    $90^{\circ}$
  • ✓
    $95^{\circ}$
  • D
    $100^{\circ}$
Answer
Correct option: C.
$95^{\circ}$
c
View full question & answer→
Question 391 Mark
In Fig , $A B$ and $C D$ are two lines intersecting at point $O$. Which one of the following statements is false?
(a) $\angle A O C$ and $\angle B O D$ are adjacent angles
(b) $\angle A O C$ and $\angle C O B$ form a linear pair
(c) $\angle A O D$ and $\angle D O B$ are supplementary angles
(d) $\angle C O B$ and $\angle A O D$ is a pair of vertically opposite angles
Image
Answer
A. $\angle A O C$ and $\angle B O D$ are adjacent angles
From Fig. , we observe that $\angle A O D$ and $\angle C O B$ form a pair of vertically opposite angles. So, statement (d) is true. Since $A O B$ is a straight line. Therefore,$
\begin{aligned}
& \angle A O D+\angle D O B=180^{\circ} \\
\Rightarrow \quad & \angle A O D \text { and } \angle D O B \text { are supplementary angles. }
\end{aligned}
$
Therefore, option (c) is true.
Clearly, $\angle A O C$ and $\angle C O B$ form a linear pair. So, option (b) is also true.
$\angle A O C$ and $\angle B O D$ are vertically opposite angles. So, statement in option (a) is false
View full question & answer→
MCQ 401 Mark
If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 2/3 then the measure of the larger angle, is
  • A
    $54^{\circ}$
  • B
    $120^{\circ}$
  • ✓
    $108^{\circ}$
  • D
    $136^{\circ}$
Answer
Correct option: C.
$108^{\circ}$
c
View full question & answer→
MCQ 411 Mark
If the measures of two supplementary angles are $(3 x+15)^{\circ}$ and $(2 x+5)^{\circ}$, then $x=$
  • A
    32
  • B
    64
  • C
    14
  • D
    24
Answer
A. 32
we have,
$
3 x+15+2 x+5=180 \Rightarrow 5 x+20=180 \Rightarrow 5 x=160 \Rightarrow x=32
$
View full question & answer→
MCQ 421 Mark
If supplement of an angle is three times its complement, then the measure of the angle is
  • A
    $45^{\circ}$
  • B
    $40^{\circ}$
  • C
    $90^{\circ}$
  • D
    $50^{\circ}$
Answer
A. $45^{\circ}$
 Let the degree measure of the required angle be $x$. Then, the measures of its supplement and complement are $180^{\circ}-x$ and $90^{\circ}-x$ respectively.
It is given that$
180^{\circ}-x=3\left(90^{\circ}-x\right) \Rightarrow 2 x=90^{\circ} \Rightarrow x=45^{\circ}
$
View full question & answer→
MCQ 431 Mark
Given $\angle P O R=3 x$ and $\angle Q O R=2 x+10^{\circ}$. If POQ is a straight line, then the value of x is
  • A
    $30^{\circ}$
  • ✓
    $34^{\circ}$
  • C
    $36^{\circ}$
  • D
    none of these
Answer
Correct option: B.
$34^{\circ}$
b
View full question & answer→
MCQ 441 Mark
Consider the following statements: When two straight lines intersect:
(i) adjacent angles are complementary
(ii) adjacent angles are supplementary
(iii) opposite angles are equal
(iv) opposite angles are supplementary
Of these statements
  • A
    (i) and (iii) are correct
  • ✓
    (ii) and (iii) are correct
  • C
    (i) and (iv) are correct
  • D
    (ii) and (iv) are correct
Answer
Correct option: B.
(ii) and (iii) are correct
b
View full question & answer→
MCQ 451 Mark
AB and CD are two parallel lines. PQ cuts AB and CD at E and F respectively. EL is the bisector of $\angle F E B$. If $\angle L E B=35^{\circ}$, then $\angle C F Q$ will be
  • A
    $55^{\circ}$
  • B
    $70^{\circ}$
  • ✓
    $110^{\circ}$
  • D
    $130^{\circ}$
Answer
Correct option: C.
$110^{\circ}$
c
View full question & answer→
Generate Paper FreeAll Lines And Angles [NEW] topics
M.C.Q - Maths STD 9 Questions - Vidyadip