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MATHS M.C.Q. [1 Marks Each]

The Triangle and Its Properties · Gujarat Board (GSEB) STD 7 (GSEB - English Medium). 12 questions.

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M.C.Q. [1 Marks Each]

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12 questions · timed · auto-graded

MCQ 11 Mark
In the given figure, DEF is a right angled triangle with $\angle E=90^{\circ}$. What type of angles are $\angle D$ and $\angle F$ ?
Image
  • A
    They are equal angles
  • B
    They form a pair of adjacent angles
  • ✓
    They are complementary angles
  • D
    They are supplementary angles
Answer
Correct option: C.
They are complementary angles
C
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MCQ 21 Mark
The sides of a triangle have length (in cm) 10, 6.5 and a, where a is a whole number. The minimum value that a can take is
  • A
    6
  • B
    5
  • C
    3
  • ✓
    4
Answer
Correct option: D.
4
D
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MCQ 31 Mark
The measures of $\angle x$ and $\angle y$ in the given figure are respectively
Image
  • A
    $30^{\circ}, 60^{\circ}$
  • B
    $40^{\circ}, 40^{\circ}$
  • C
    $70^{\circ},70^{\circ}$
  • ✓
    $70^{\circ}, 60^{\circ}$
Answer
Correct option: D.
$70^{\circ}, 60^{\circ}$
D
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MCQ 41 Mark
If the exterior angle of a triangle is $130^{\circ}$ and its interior opposite angles are equal, then measure of each interior opposite angle is
  • A
    $55^{\circ}$
  • ✓
    $65^{\circ}$
  • C
    $50^{\circ}$
  • D
    $60^{\circ}$
Answer
Correct option: B.
$65^{\circ}$
B
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MCQ 51 Mark
The top of a broken tree touches the ground at a distance of 8 m from its base. If the tree is broken at a height of 6 m from the ground, then the actual height of the tree is
Image
  • A
    15 m
  • B
    14 m
  • ✓
    16 m
  • D
    17 m
Answer
Correct option: C.
16 m
(C) 16 cm
Hint : Let $D C B$ be the tree. The tree is broken at point $C$ such that $B C=6 m$ and its top $D$ touches the ground at $A$.
Then, $D C=A C$
Thus, $\triangle A B C$ is a right angled triangle, right angled at $B$ such that $A B=8 m, B C=6 m$.
In $\triangle A B C$, by Pythagoras property,
$(A C)^2  =(B C)^2+(A B)^2 $
$(A C)^2 =(6)^2+(8)^2 $
$(A C)^2 =36+64 $
$(A C)^2  =100 $
$\Rightarrow$$\quad$$A C  =\sqrt{100}=10 $
$\because$$\quad$$A C  =D C=10 m $
$\therefore$$\quad$$B D =B C+C D=(6+10) m $
$\quad$$\quad$$\quad$$=16 m$
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MCQ 61 Mark
In a right angled $\triangle A B C$ if $\angle B=90^{\circ}, B C=3 cm$ and $A C=5 cm$, then the length of side $A B$ is
  • A
    3 cm
  • ✓
    4 cm
  • C
    5 cm
  • D
    6 cm
Answer
Correct option: B.
4 cm
B
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MCQ 71 Mark
In the given figure, find the value of x
Image
  • A
    $75^{\circ}$
  • B
    $90^{\circ}$
  • ✓
    $120^{\circ}$
  • D
    $60^{\circ}$
Answer
Correct option: C.
$120^{\circ}$
(C) $120^{\circ}$
Hint : In $\triangle A B C$
$\angle A+\angle B+\angle A C B=180^{\circ}$ $\quad$[angle sum property of a triangle]
$\therefore \angle A C B=180^{\circ}-\left(25^{\circ}+35^{\circ}\right)=120^{\circ}$
Now, $\angle A C D+\angle A C B=180^{\circ}$ $\quad$[linear pair]
$\therefore \quad \angle A C D=180^{\circ}-120^{\circ}=60^{\circ}$
So, $x=\angle O C D+\angle C D O$$\quad$[exterior angle of a triangle]
$x=60^{\circ}+60^{\circ}$
Hence, $x=120^{\circ}$
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MCQ 81 Mark
In the following figure, $B C=C A$ and $\angle A=20$, then $\angle A C D$ is equal to
Image
  • A
    $30^{\circ}$
  • ✓
    $40^{\circ}$
  • C
    $60^{\circ}$
  • D
    $80^{\circ}$
Answer
Correct option: B.
$40^{\circ}$
(B) $40^{\circ}$
Hint $\because B C=C A$ $\angle B A C=\angle A B C [\because$ the angles opposite to equal sides of a triangle are equal]
So, $\angle B A C=\angle A B C=20^{\circ}$
Now, $\angle A C D=\angle B A C+\angle A B C$ $[\because$ exterior angle is equal to sum of interior opposite angles]
Hence, $\angle A C D=20^{\circ}+20^{\circ}=40^{\circ}$
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MCQ 91 Mark
The perimeter of the rectangle whose length is 24 cm and a diagonal is 26 cm, is
  • A
    50 cm
  • B
    34 cm
  • C
    48 cm
  • ✓
    68 cm
Answer
Correct option: D.
68 cm
D
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MCQ 101 Mark
Which of the following cannot be the length of the third side of a triangle, whose two sides measure 10 cm and 5 cm?
  • A
    12 cm
  • ✓
    16 cm
  • C
    14 cm
  • D
    13 cm
Answer
Correct option: B.
16 cm
(B) 16 cm
Hint : Let $x$ can be the length of the third side. We know that the sum of lengths of two sides of a triangle is greater than the length of third side.
$\therefore 10$ $cm+5$ $cm>x$ $cm \Rightarrow 15>x$ $cm$
Hence, option (b) is answer.
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MCQ 111 Mark
In a $\triangle A B C$, if $\angle A=60^{\circ}$ and $\angle B=30^{\circ}$, then the exterior angle formed by producing $B C$ is equal to
  • A
    $180^{\circ}$
  • B
    $99^{\circ}$
  • ✓
    $90^{\circ}$
  • D
    $105^{\circ}$
Answer
Correct option: C.
$90^{\circ}$
C
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MCQ 121 Mark
In a $\triangle A B C, A D$ is the bisector of $\angle A$ meeting $B C$ at $D$, $C F \perp A B$ and $E$ is the mid-point of $A C$. Then, median of the triangle is
  • A
    AD
  • ✓
    BE
  • C
    FC
  • D
    DE
Answer
Correct option: B.
BE
B
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