Exterior Angle Theorem

Q.

Two angles of a polygon are right angles and every other angle is 120 degree. Find the number of sides of the polygon.

Q.

THE EXTERIOR ANGLE OF A PENTAGON ARE IN THE RATIO 1:2:3:4:5. FIND ALL THE INTERIOR ANGLES OF THE PENTAGON.

Q.

Question 9
In the given figure, the value of x is

(a) ${110}^{\circ }$
(b) ${46}^{\circ }$
(c) ${64}^{\circ }$
(d) ${150}^{\circ }$

Q.

The measures of angles of hexagon are x°, x-5°, 2x-5°,

2x+20°.

Find x.

Q.

Is it possible to have a regular polygon if each interior angle is $125°$

Q.

Find out if it is possible with each interior angle equal to 105°

Q.

How do we find the measure of EACH exterior angle and the measure of EACH interior angle of any polygon?

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

Q.

Sum of the measure of the exterior angles of a decagon is ______ .

1. 360^o

2. 270^o

3. 90^o

4. 180^o

Q.

In the given figure , name the points which lie in the exterior of $\Delta ABC$ .

Q.

In the figure, sides QP and RQ of $\Delta$PQR are produced to points S and T respectively. If $\angle$SPR = ${135}^{\circ }$ and $\angle$PQT = ${110}^{\circ }$ find 2$\angle$PRQ.

1. 

2. 

3. 

4. 

Q. What is the sum of all exterior angles of a triangle?

Q.

In the figure, sides QP and RQ of $\Delta$PQR are produced to points S and T, respectively. If $\angle$SPR = ${135}^{\circ }$ and $\angle$PQT = ${110}^{\circ }$, find 2$\angle$PRQ.

1. 

2. 

3. 

4. 

Q.

In fig $x=$ ${30}^{\circ }$ the value of $(6y–3x)$ is

1. ${180}^{\circ }$

2. ${60}^{\circ }$

3. ${150}^{\circ }$

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

Q.

Each interior angle of a polygon is $120°$. Find the number of sides.

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).

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Q.

Question 65

State whether the statement is True or False.

Two angles making a linear pair are always adjacent angles.

Q. Solve this:
Q. Find the measure of each exterior angle of a regular polygon of18 sides.

Q. (a) Find $x+y+z$
(b) Find $x+y+z+w$

Q. Question 12
If S is a point on side PQ of a $\Delta$ PQR such that PS = QS = RS, then

(A) $PR.QR=R{S}^2$
(B) $Q{S}^2+R{S}^2=Q{R}^2$
(C) $P{R}^2+Q{R}^2=P{Q}^2$
(D)​​​​​​​ $P{S}^2+R{S}^2=P{R}^2$​​​​​​​

Q.

Consider the figure:

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

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Q.

In the given figure, m = ___.

1. ${20}^{\circ }$

2. ${10}^{\circ }$

3. ${30}^{\circ }$

4. ${40}^{\circ }$

Q.

Question 33

In the given figure, $a={40}^{\circ }$. The value of b is

(a) ${20}^{\circ }$
(b) ${24}^{\circ }$
(c) ${36}^{\circ }$
(d) ${120}^{\circ }$

Q.

Can exterior angle of 22 be an interior angle of a regular polygon

how will we solve it?

Q.

Find the value of the unknown exterior angle $x$in the following diagram.

Q. In the figure given below, measure of $\angle ABC$ is

1. ${80}^0$
2. ${70}^0$
3. ${60}^0$
4. ${50}^0$

Q.

One of the exterior angles of a triangle $70°$and the interior opposite angles are in the ratio $3:4$ Find the angles of the triangle.

Q.

Consider the figure:

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

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