Sample QuestionsTriangle And Its Angles questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
In Fig. $AB$ and $CD$ are parallel lines and transversal $EF$ intersect them at $P$ and $Q$ respectively. If $\angle\text{APR}=25^\circ,\angle\text{RQC}=30^\circ$ and $\angle\text{CQF}=65^\circ,$ then:
- ✓
$x = 55^\circ , y = 40^\circ $
- B
$x = 50^\circ , y = 45^\circ $
- C
$x = 60^\circ , y = 35^\circ$
- D
$x = 35^\circ , y = 60^\circ$
Answer: A.
View full solution →In Fig. if $l_1$ || $l_2$, the value of $x$ is:
- A
$22\frac{1}{2}$
- B
$30$
- ✓
$45$
- D
$60$
Answer: C.
View full solution →In a $\triangle\text{ABC},$ if $\angle\text{A}=60^\circ,\angle\text{B}=80^\circ$ and the bisectors of $\angle\text{B}$ and $\angle\text{C}$ meet at $O$, then $\angle\text{BOC}=$
- A
$60^\circ$
- ✓
$120^\circ$
- C
$150^\circ$
- D
$30^\circ$
Answer: B.
View full solution →In Fig. $x + y =$
- A
$270^\circ$
- ✓
$230^\circ$
- C
$210^\circ$
- D
$190^\circ$
Answer: B.
View full solution →In $\triangle\text{ABC},\angle\text{B}=\angle\text{C}$ and ray $AX$ bisects the exterior angle $\angle\text{DAC}.$ If $\angle\text{DAX}=70^\circ$ then $\angle\text{ACB}=$
- A
$35^\circ$
- B
$90^\circ$
- ✓
$70^\circ$
- D
$55^\circ$
Answer: C.
View full solution →Statement-1 (A): In a $\triangle A B C$, if $\angle A=65^{\circ}$ and $\angle C=30^{\circ}$, then AC is the longest side of $\triangle A B C$.
Statement-2 (R) : Sum of the angles of a triangle is $180^{\circ}$.
- A
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- ✓
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- C
Statement-1 is true, Statement-2 is false.
- D
Statement-1 is false, Statement-2 is true.
Answer: B.
View full solution →Statement-1 (A): It is possible to construct a triangle with lengths of its sides as 8 cm, 7 cm and 4 cm .
Statement-2 (R): The sum of any two sides of a triangle is greater than the third side.
- ✓
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- B
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- C
Statement-1 is true, Statement-2 is false.
- D
Statement-1 is false, Statement-2 is true.
Answer: A.
View full solution →Statement-1 (A): It is not possible to construct a triangle with lengths of its sides as 9 cm , 7 cm and 17 cm .
Statement-2 (R): The difference of any two sides of a triangles is less than the third side.
- A
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- ✓
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- C
Statement-1 is true, Statement-2 is false.
- D
Statement-1 is false, Statement-2 is true.
Answer: B.
View full solution →Statement-1 (A): In a $\triangle A B C$, the bisectors of $\angle B$ and $\angle C$ meet a point $O$ and the bisectors of ext $\angle B$ and ext $\angle C$ meet a point $O^{\prime}$. If $\angle B O C=135^{\circ}$, then $\angle B O^{\prime} C=45^{\circ}$
Statement-2 (R): In a $\triangle A B C$, if the bisectors of $\angle B$ and $\angle C$ meet at a point $O$ and the bisectors of ext $\angle B$ and ext $\angle C$ meet at a point $O^{\prime}$. Then, $\angle B O C$ and $\angle B O^{\prime} C$ are supplementary.
- ✓
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- B
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- C
Statement-1 is true, Statement-2 is false.
- D
Statement-1 is false, Statement-2 is true.
Answer: A.
View full solution →Statement-1 (A): In Fig., if the bisectors of angles $\angle B$ and $\angle C$ of $\triangle A B C$ meet at $O$, then $\angle B O C=140^{\circ}$
Statement-2 (R): If bisectors of angles $B$ and $C$ of a $\triangle A B C$ meet at $O$, then $\angle B O C=90^{\circ}+\frac{\angle A}{2}$
- A
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- B
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- C
Statement-1 is true, Statement-2 is false.
- ✓
Statement-1 is false, Statement-2 is true.
Answer: D.
View full solution →The following statements are true $(T)$ and which are false $(F):$
An exterior angle of a triangle is equal to the sum of the two interior opposite angles.
View full solution →The following statements are true $(T)$ and which are false $(F):$
An exterior angle of a triangle is greater than the opposite interior angles.
View full solution →The following statements are true $(T)$ and which are false $(F):$ Sum of the three angles of a triangle is $180^\circ .$
View full solution →The following statements are true $(T)$ and which are false $(F): $ All the angles of a triangle can be equal to $60^\circ .$
View full solution →The following statements are true $(T)$ and which are false $(F):$ A triangle can have two obtuse angles.
View full solution →Fill in the blanks to make the following statements true: An exterior angle of a triangle is equal to the two ______ opposite angles.
Fill in the blanks to make the following statements true: Sum of the angles of a triangle is _______
Fill in the blanks to make the following statements true: A triangles cannot have more than ______ obtuse angles.
Fill in the blanks to make the following statements true: A triangle cannot have more than ______ right angles.
Fill in the blanks to make the following statements true: An exterior angle of a triangle is always _______ than either of the interior opposite angles.
In Fig. if AB = AC and angle B = angle C. Prove that BQ = CP
Prove that the sum of three altitudes of a triangle is less than the sum of its sides.
CDE is an equilateral triangle formed on a side CD of a square ABCD. Show that $\triangle A D E \cong \triangle B C E$.
View full solution →Find the measure of each angle of an equilateral triangle.
ABC is an isosceles triangle in which AB = AC BE and CF are its two medians. Show that BE = CF
Can a triangle have: Two acute angles? Justify your answer in case.
Can a triangle have: All angles equal to $60^\circ ?$ Justify your answer in case.
View full solution →Can a triangle have: All angles more than $60^\circ ?$ Justify your answer in case.
View full solution →Write the sum of the angles of an obtuse triangle.
The exterior angles, obtained on producing the base of a triangle both ways are $104^\circ$ and $136^\circ$. Find all the angles of the triangle.
View full solution →In figure $AE$ bisects $\angle\text{CAD}$ and $\angle\text{B}=\angle\text{C}.$ Prove that $AE\ ||\ BC$.
View full solution →In a $\triangle\text{ ABC},\text{ AD}$ bisects $\angle\text{A}$ and $\angle\text{C} > \angle\text{B}.$. Prove that $\angle\text{ADB} > \angle\text{ADC}.$
View full solution →In Fig. $\text{AC}\perp\text{CE}$ and $\angle\text{A}:\angle\text{B}:\angle\text{C}=3:2:1,$ find the value of $\angle\text{ECD}.$ 
View full solution →Two angles of a triangle are equal and the third angle is greater than each of those angles by $30^\circ$. Determine all the angles of the triangle.
View full solution →In a $\triangle\text{ABC},$ the internal bisectors of $\angle\text{B}$ and $\angle\text{E}$ meet at $P$ and the external bisectors of $\angle\text{B}$ and $\angle\text{C}$ meet at $Q.$ Prove that $\angle\text{BPC}+\angle\text{BQC}=180^\circ.$
View full solution →In $\triangle\text{ABC},$ if bisectors of $\angle\text{ABC}$ and $\angle\text{ACB}$ intersect at $O$ at angle of $120^\circ ,$ then find the measure of $\angle\text{A}.$
View full solution →In Fig. the sides $BC, CA$ and $AB$ of a triangle $ABC$ have been produced to $D, E$ and $F$ respectively. If $\angle\text{ACD}=105^\circ$ and $\angle\text{EAF}=45^\circ,$ find all the angles of the triangle $ABC.$ 
View full solution →In Fig. $\text{AM}\perp\text{BC}$ and $AN$ is the bisector of $\angle\text{A}.$ If $\angle\text{B}=65^\circ$ and $\angle\text{C}=33^\circ,$ find $\angle\text{MAN}.$
View full solution →$ABC$ is a triangle. The bisector of the exterior angle at $B$ and the bisector of $\angle\text{C}$ intersect each other at $D$. Prove that $\angle\text{D}=\frac{1}{2}\angle\text{A}.$
View full solution →A ladder manufacturing company manufactures foldable step ladders of aluminum as shown in Fig. The lengths of two legs AB and AC are both equal to 110 cm and the angle between the two legs is $30^{\circ}$. On the basis of the above information answer the following questions:
(i) $\angle A B C$ is equal to
(a) $70^{\circ}$ $\quad$(b) $75^{\circ}$(c) $85^{\circ}$ $\quad$(d) $60^{\circ}$
(ii) If $\angle B A C=60^{\circ}$, then $B C=$
(a) 120 cm $\quad$(b) 55 cm $\quad$(c) 110 cm $\quad$(d) 100 cm
(iii) $\triangle A B C$ is
(a) isosceles acute angled $\quad$ (b) right angled isosceles
(c) isosceles obtuse angled$\quad$(d) equilateral
(iv) In two triangles ABC and DEF, if $\angle A=\angle D, A B=D E$ and $A C=D F$, then the criterion by which two triangles are congruent is
(a) SSS $\quad$(b) ASA $\quad$(c) AAS $\quad$(d) SAS View full solution →Engineers often use the familiar triangular shape for strength in bridge design. Triangles are effective tools for architecture and are used in the design of bridges, buildings and other structures as they provide strength and stability. The triangle is common in all sorts of building supports and trusses. Following are some questions on triangles:
(i) In triangles ABC and DEF, if AB = DE, AC = EF and $\angle A=\angle E$. Then,
(a) $\triangle A B C \cong \triangle D E F$ by SAS criterion $\quad$(b) $\triangle A B C \cong \triangle E F D$ by SSS criterion
(c) $\triangle A B C \cong \triangle E D F$ by SAS criterion $\quad$(d) $\triangle A B C \cong \triangle E D F$ by ASA criterion
(ii) If $\triangle P R Q \cong \triangle D E F$, then $D E=$
(a) PR $\quad$(b) RQ $\quad$(c) PQ $\quad$(d) DF
(iii) Is it possible to construct a triangle with lengths of sides as 5 cm, 4 cm and 10 cm ?
(iv) In triangles ABC and DEF, AB = FD and $\angle A=\angle D$. Then the two triangles will be congruent by SAS axiom, if
(a) BC = EF $\quad$(b) AC = DE $\quad$(c) AC = EF $\quad$(d) BC = DE View full solution →In the given figure, if $\text{AB }||\text{ DE}$ and $\text{BD }||\text{ FG}$ such that $\angle\text{FGH}=125^\circ$ and $\angle\text{B}=55^\circ,$ find $x$ and $y.$
View full solution →If the bisectors of the base angles of a triangle enclose an angle of $135^\circ $, prove that the triangle is a right angle.
View full solution →The bisectors of base angles of a triangle cannot enclose a right angle in any case.
In the given figure, side $BC$ of $\triangle\text{ABC}$ is produced to point $D$ such that bisectors of $\angle\text{ACD}$ meet at a point $E$. If $\angle\text{BAC}=68^\circ,$ find $\angle\text{BEC}.$
View full solution →If the side $BC$ of $\triangle\text{ABC}$ is produced on both sides, then write the difference between the sum of the exterior angles so formed and $\angle\text{A}.$
View full solution →