Exterior Angle Property

Q.

A triangle has _____ exterior angles

1. 4

2. 6

3. 3

4. 2

Q.

In the figure, sides $QP$ and $RQ$ of $△PQR$ are produced to points $S$ and $T,$ respectively. If $\angle SPR={135}^{\circ }$ and $\angle PQT={110}^{\circ }$, find $\angle PRQ.$

1. ${90}^{\circ }$

2. ${150}^{\circ }$

3. ${110}^{\circ }$

4. ${65}^{\circ }$

Q.

In figure, $\angle ACD={120}^{\circ }$ and $\angle APB={100}^{\circ }$ ,
(i) find x and y.
(ii) If $\angle BAC=2.5y,$ find $\angle ABC$.
[4 MARKS]

Q.

In an isosceles triangle, one of the equal angles measures ${50}^{\circ }$. The sum of all the exterior angles of the same triangle is ___ (in degrees)​.

Q. If the opposite interior angles of an exterior angle of measure $123°$ is $x$ and $x+3$, then $x$=

1. 40°
2. 60°
3. 80°

Q.

Find the value of $△$ BAC in the given figure.

1. 58°

2. 44°

3. 55°

4. 65°

Q.

In the given figure, AB = AC, $\angle ABE={120}^{\circ }$ The value of $x$ = ___

1. ${70}^{\circ }$

2. ${55}^{\circ }$

3. ${65}^{\circ }$

4. ${60}^{\circ }$

Q.

In the given figure, $\angle CAE={84}^{\circ }$. If $\angle B:\angle C=3:4,$ then $\angle B$ = ___ and $\angle C$ = ___,

1. $\angle B={27}^{\circ },\angle C={36}^{\circ }$

2. $\angle B={36}^{\circ },\angle C={48}^{\circ }$

3. $\angle B={75}^{\circ },\angle C={90}^{\circ }$

4. $\angle B={33}^{\circ },\angle C={44}^{\circ }$

Q. ABC is a triangle in which AB = AC. The base BC is produced to D. If $\angle$ACD = ${130}^{\circ }$, then $\angle$A = ___.

1. 80°

2. 60°

3. 50°

4. 40°

Q. Find the value of $x$ in the adjoining figure.

Q.

Consider the figure:

If BC = AC, x = 2y, and angle ∠ACB = 60^o, then find the value of ∠x & ∠y (in degrees).

1. 100

2. $y=80$
3. $x=40$
4. $y=40$

Q. In the figure given below, find the measure of the angles denoted by $x,y,z,p,q$ and $r$.

Q.

Consider the figure:

If $\angle$A = ${50}^{\circ }$​, $\angle$B = ${70}^{\circ }$​, and x = 2y, then, find the value of x (in degrees)

1. 80°

2. 85°

3. 40°

4. 40°

Q.

Consider the figure:

If BC = AC, x = 2y, and angle ACB = 60^o, then find the value of $\angle A$ + $\angle B$ + $\angle x$ + $\angle y$ (in degrees).

___

Q. On extending the sides of a triangle, six exterior angles are formed, two at each side.

1. True
2. False

Q.

An exterior angle of a triangle is equal to the sum of two _________ angles

1. Exterior opposite

2. Interior opposite

3. Interior

4. Opposite

Q.

Consider the figure:

If $\angle$A = ${50}^{\circ }$​, $\angle$B = ${70}^{\circ }$​, and x = 2y, then find the value of y (in degrees).

___

Q. Compute the value of x in each of the following figure

Q.

Consider the figure:

If BC = AC, x = 2y, and angle ACB = 60^o, then find the value of $\angle$A + $\angle$B + $\angle$x + $\angle$y (in degrees).

___

Q. How many exterior angles does a triangle have?

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

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

Q. Using the exterior angle property, find the value of $y$ from the figure.

1. ${80}^{\circ }$
2. ${100}^{\circ }$
3. ${20}^{\circ }$
4. ${50}^{\circ }$

Q.

Consider the figure:

Find the value of x + y + $\angle$ACB.

___

Q. Answer the following questions with reference to the figure:



(1) Name the exterior angles at the vertex P.

(2) Name the angles forming a linear pair with ∠PRQ.

(3) Is ∠SQT an exterior angle of the ∆PQR? Give the reason for your answer.

(4) Name the angles of ∆PQR that form a linear pair with the exterior angle ∠PQS.

Q. Two angles are adjacent and form an angle of ${100}^{\circ }$. The larger is ${20}^{\circ }$ less than five times the smaller. The larger angle is

1. ${70}^{\circ }$
2. ${90}^{\circ }$
3. ${80}^{\circ }$
4. ${75}^{\circ }$