Exterior Angle Property

Q.

An exterior angle of a triangle is equal to the sum of two ______ .

1. interior angles
2. opposite interior angles
3. adjacent interior angles
4. opposite exterior angles

Q.

If the arms of one angle are respectively parallel to the arms of another angle, then the two angles can be:

1. Neither equal nor supplementary

2. Not equal but supplementary

3. Equal but not supplementary

4. Either equal or supplementary.

Q.
The measure of angle ACB is .

1. ${60}^{\circ }$
2. ${90}^{\circ }$
3. ${30}^{\circ }$

Q. One of the interior opposite angles of a triangle to the exterior angle 120 deg is 70 deg, find other angle.

1. 50

Q. Question 2
Bisectors of interior $\angle B$ and exterior $\angle ACD$ of a $\Delta ABC$ intersect at the point T. Prove that $\angle BTC=\frac{1}{2}\angle BAC$
Thinking process

Q.

An exterior angle of a triangle is ${115}^{\circ }$ and one of the opposite angles is ${35}^{\circ }$. Find the other two angles. [3 MARKS]

Q. Prove that exterior angle is the sum of two opposite interior angles?

Q.

The exterior angle of a triangle is equal to the sum of non-adjacent interior angles. Say true or false.

1. False

2. True

Q.

Consider two angles - $\angle$ABC and $\angle$XYZ. Following information is given about the angles:

1. $\angle$ABC and $\angle$XYZ are supplementary.
2. $\angle$ABC is acute.

Based on this information, which of the following can not be the numerical value of $\angle$XYZ?

1. 89°

2. 91°

3. 175°

4. 179°

Q.

Find $x,y,z$ in each of the following figures :

Q.

Question 8

In the given figure, PB = PD. The value of x is

a) ${85}^{\circ }$
b) ${90}^{\circ }$
c) ${25}^{\circ }$
d) ${35}^{\circ }$

Q.

Question 3

In the given figure, PQ = PS. The value of x is

a) ${35}^{\circ }$
b) ${45}^{\circ }$
c) ${55}^{\circ }$
d) ${70}^{\circ }$

Q. Find the value of $\angle A$ + $\angle B$ + $\angle C$ +$\angle D$ + $\angle E$ from the following figure.

1. ${300}^{\circ }$
2. ${180}^{\circ }$
3. ${540}^{\circ }$
4. ${360}^{\circ }$

Q.

Question 22

In the given figure, $\angle ROS$ is a right angle and $\angle POR$ and $\angle QOS$ are in the ratio 1:5. Then, $\angle QOS$ measures

(a) ${150}^{\circ }$
(b) ${75}^{\circ }$
(c) ${45}^{\circ }$
(d) ${60}^{\circ }$

Q. Find the value of $x^o$.

1. ${100}^o$
2. ${120}^o$
3. ${110}^o$
4. ${130}^o$

Q.

Question 2 (ii)
Find the value of the unknown interior angle x in the following figures.

Q.

Question 2 (ii)
In the adjoining figure, identify:

The pairs of alternate interior angles.

Q.

Consider the figure:

If $\angle$A = ${50}^{\circ }$​, $\angle$B = ${70}^{\circ }$​ and x = 2y, then x+y is equal to (in degrees)

__

Q. In the given triangle AC = BC, find angles x and y, as shown in the figure.

Q. Question 3
An exterior angle of a triangle is ${105}^{\circ }$ and its two interior opposite angles are equal. Each of these equal angles is:

A) $37{\frac{1}{2}}^{\circ }$
B) $52{\frac{1}{2}}^{\circ }$
C) $72{\frac{1}{2}}^{\circ }$
D) ${75}^{\circ }$​​​​​​​

Q.

Find the value of the unknown interior angle x in the following figures:

Q.

Find the value of x, y and z in the figure given below.

Q. In the given figure, AB and CD are parallel lines and XY is a transversal to them. If ∠APX = 110°, ∠XPB = (m+10)°, ∠PQC = (n-20)°, ∠PQD = 70°, find the value of m+n.

1. 60
2. 190
3. 130
4. 170

Q.

Sum of an exterior angle of a triangle and adjacent interior angle is __________.

1. 360⁰

2. 180⁰

3. 240⁰

4. 90⁰

Q. $\text{In}\Delta ABC,\text{the measure of}\angle ACD\text{is}{105}^{\circ }.$
$\text{If}\angle B={65}^{\circ },\text{then find}\angle A.$

1. ${35}^{\circ }$
2. ${30}^{\circ }$
3. ${40}^{\circ }$
4. ${50}^{\circ }$

Q. The total angle measuring around a point is ___

1. ${360}^{\circ }$
2. ${180}^{\circ }$
3. ${120}^{\circ }$
4. ${5400}^{\circ }$

Q. Question 4
In $\Delta ABC$, if BC =AB and $\angle B={80}^{\circ }$ then $\angle A$ is equal to
(A) ${80}^{\circ }$
(B) ${40}^{\circ }$
(C) ${50}^{\circ }$
(D) ${100}^{\circ }$

Q.

The two interior opposite angles of an exterior angle of a triangle are 60 degree and 80 degree. Find the measure of the exterior angle.

Q.

Sum of all the exterior angles formed by producing the sides of the triangle is

1. 360⁰

2. 180⁰

3. 540⁰

4. 150⁰

Q.

Question 14 (iv)
In the adjoining figure, name the following pairs of angles:
Unequal supplementary angels.