Angle Sum Property of a Triangle

Q.

If the angles of a triangle are in the ratio 1 : 2 : 3, determine three angles.

Q.

The angles of a triangle are $(x-40{)}^{\circ },(x-20{)}^{\circ }$ and ${(\frac{1}{2}x-10)}^{\circ }$. Find the value of $x$.

Q.

If one angle of a triangle is equal to the sum of the other two, show that the triangle is a right triangle.

Q.

$\text{It is given that}\Delta ABC\cong \Delta FDE\text{in which AB = 5 cm,}\angle B={40}^{\circ },\angle A={80}^{\circ }\text{and FD = 5 cm. Then, which of the following is true?}\left(a\right)\angle D={60}^{\circ }\left(b\right)\angle E={60}^{\circ }\left(c\right)\angle F={60}^{\circ }\left(d\right)\angle D={80}^{\circ }$

Q.

$In\Delta ABC,\angle A={40}^{\circ }and\angle B={60}^{\circ }.\text{Then, the longest side of}\Delta ABCis\left(a\right)BC\left(b\right)AC\left(c\right)AB\left(d\right)\text{cannot be determined}$

Q.

If bisectors of $\angle Aand\angle B$ of a quadrilateral ABCD intersect each other at P, of $\angle Band\angle C$ at Q, of $\angle Cand\angle D$ at R and of $\angle Dand\angle A$ at S then PQRS is a

(a) rectangle

(b) parallelogram

(c) rhombus

(d) quadrilateral whose opposite angles are supplementary

Q.

Two angles of a triangle are equal and the third angle is greter than each of those angles by ${30}^{\circ }$. Determine all the angles of the triangle.

Q.

The angles of a triangle are arranged in ascending order of magnitude. If the difference between two consecutive angle is ${10}^{\circ }$, find the three angles.

Q.

The angle of a triangle are in the ratio 2 : 3 : 4. The largest angle of the triangle is

(a) ${120}^{\circ }$

(b) ${100}^{\circ }$

(c) ${80}^{\circ }$

(d) ${60}^{\circ }$

Q.

Which is true?

(a) A triangle can have two right angles.

(b) A triangle can have two obtuse angles.

(c) A triangle can have two acute angles.

(d) An exterior angle of a triangle is less than either of ther interior opposite angles.

Q.

Find the measures of angle marked by the letters in the following diagram.parallel lines are marked by double arrows

Q. Prove that in $△ABC$, $tan\left(\frac{B+C}{2}\right)=cot\left(\frac{A}{2}\right)$ .

Q.

In the figure given below, if lines PQ and RS intersect at point T, such that,
$\angle PRT={40}^{\circ }$, $\angle RPT={95}^{\circ }$ and $\angle TSQ={75}^{\circ }$, then find $2\angle SQT$.

1. ${150}^{\circ }$

2. ${80}^{\circ }$

3. ${90}^{\circ }$

4. ${120}^{\circ }$

5. None of the above

Q.

$△ABC\mathrm{and}△DBC$ are two isosceles triangles on the same base $BC.$ Show that $\angle \mathrm{ABD}=\angle \mathrm{ACD}$.

Q.

If the angles of a triangle are in the ratio 2 : 1 : 3. Then find the measure of smallest angle.

Q.

The sum of two angles of a triangle is ${80}^{\circ }$ and their difference is ${20}^{\circ }$. Find all the angles. [4 MARKS]

Q.

In $\Delta$ ABC, D is a point on BC such that AB= AD = BD =DC. Show that : $\angle$ ADC : $\angle$ C = 4: 1.

Q.

$\text{In the given figure}AD\perp BCandCD>BD.ShowthatAC>AB.$

Q.

In the figure $AD\parallel BC$, find the value of x

Q. The measures of the angles of a triangle are in the ratio $5:4:3$. Find the angles of the triangle.

Q. Question 6
It is given that $\angle XYZ={64}^{\circ }$ and XY is produced to point P. Draw a figure from the given information. If a ray YQ bisects $\angle ZYP,$ find $\angle XYQ$ and reflex $\angle QYP.$

Q. The angles of the triangle are 3x–40, x+20 and 2x–10 then the value of x is_________.

Q.

$Ina\Delta ABC,if3\angle A=4\angle B=6\angle CthenA:B:C=?$

(a) 3:4:6 (b) 4:3:2 (c) 2:3:4 (d) 6:4:3

Q. Question 3
ABCD is a rhombus such that $\angle ACB={40}^{\circ }$, then $\angle ADB$ is
(a) ${40}^{\circ }$
(b) ${45}^{\circ }$
(c) ${50}^{\circ }$
(d) ${60}^{\circ }$

Q. In the given figure, find the value of 'z'.

Q.

$In\Delta ABC,\text{BC = AB and}\angle B={80}^{\circ }.Then,\angle A=?\left(a\right){50}^{\circ }\left(b\right){40}^{\circ }\left(c\right){100}^{\circ }\left(d\right){80}^{\circ }$

Q. In the figure below lines A'A" and C'C" are parallel. AB is the bisector of $\angle$CAA" and BC is the bisector of $\angle$ ACC". What is the measure of $\angle$ABC?

1. 70°
2. 80°
3. 90°
4. 60°

Q.

$Ina\Delta ABC,if\angle A-\angle B={42}^{\circ }and\angle B-\angle C={21}^{\circ }then\angle B=?\left(a\right){32}^{\circ }\left(b\right){63}^{\circ }\left(c\right){53}^{\circ }\left(d\right){95}^{\circ }$

Q.

In a parallelogram ABCD,

$A=\left(2x+20\right)°,B=\left(3x-30\right)°$. Find the value of $x.$

Q. The angles of a triangle are arranged in ascending order of magnitude. If the difference between two consecutive angles is ${10}^{\circ }$, find the three angles.