#### Solved Examples and Worksheet for Exterior Angle Theorem

Q1Find the value of x, if y = 55° and z = 65°. A. 115°
B. 125°
C. 60°
D. 120°

Step: 1
CAB + ABC + ACB = 180°
[Sum of the interior angles of a triangle is 180°.]
Step: 2
55° + 65° + ACB = 180°
[Substitute.]
Step: 3
120° + ACB = 180°
Step: 4
ACB = 60°
[Subtract 120 on both the sides.]
Step: 5
ACD + ACB = 180°
[Angle made by a straight line is 180°.]
Step: 6
x + 60° = 180°
[Substitute.]
Step: 7
x = 120°
[Subtract 60 on both the sides.]
Step: 8
So, the value of x is 120°.
Q2In triangle ABC, x = 30° and y = 50°. Find the measure of CBD. A. 30
B. 80
C. 100
D. 50

Step: 1
In ΔABC, CBD = ACB + CAB
[Exterior angle theorem.]
Step: 2
m CBD = 50 + 30
[Substitute.]
Step: 3
m CBD = 80
Q3What is the value of z + y? A. 120
B. 150
C. 180
D. 200

Step: 1
z + 60 = 180
[Linear pair.]
Step: 2
z = 180 - 60 = 120
Step: 3
The sum of the measures of the angles of a triangle is 180.
[Triangle angle sum theorem.]
Step: 4
y + 60 + 90 = 180
[From step 3.]
Step: 5
y = 180 - (60 + 90) = 30
[Simplify.]
Step: 6
So, z + y = 120 + 30 = 150
Q4Find the value of x, if y = 55 and z = 65. A. 115
B. 120
C. 60
D. 125

Step: 1
ACB = 180o - (55o + 65o) = 60o
Step: 2
ACD = xo = 180o - 60o = 120o
Step: 3
So, the value of x is 120.
Q5What is the measure of the marked exterior angle of the triangle?[Given x = 54° and y = 86°.] A. 40
B. 126
C. 140
D. 94

Step: 1
In ΔABC, mABC = 54 and mBAC = 86
Step: 2
Since side BC is extended to the point D, exterior angle of ACB is ACD.
Step: 3
The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.
[Exterior angle theorem.]
Step: 4
mABC + mBAC = mACD
[From step 3.]
Step: 5
54 + 86 = mACD
[Substitute the values of ABC and BAC.]
Step: 6
mACD = 140
[Simplify.]
Step: 7
So, the measure of the marked exterior angle of the triangle is 140.
Q6Find the value of x in the figure if ABD = 108° and a = 54. A. 108°
B. 18°
C. 92°
D. 72°

Step: 1
From the figure, BAC = 90° and ABD = 108°.
Step: 2
The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.
[Exterior angle theorem.]
Step: 3
BAC + ACB = ABD
[From step 2.]
Step: 4
90° + (x - 54)° = 108°
[Substitute.]
Step: 5
36° + x = 108°
Step: 6
x = 72°
[Subtract 36 from both sides.]
Step: 7
So, the value of x in the figure is 72°.
Q7What is the measure of y in the figure? [Given x = 63 and ABD = 136.] A. 73°
B. 136°
C. 44°
D. 63°

Step: 1
From the figure, CAB = 63° and ABD = 136°.
Step: 2
The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.
[Exterior Angle Theorem.]
Step: 3
CAB + ACB = ABD
[From step 2.]
Step: 4
63° + y° = 136°
[Substitute.]
Step: 5
ACB = y° = 136° - 63°
[Subtract.]
Step: 6
So, the measure of y is 73°.
Q8Find the measure of x. A. 20°
B. 50°
C. 130°
D. 25°

Step: 1
If one side of a triangle is produced, then the exterior angle so formed is equal to the sum of the interior opposite angles.
Step: 2
ACD = BAC + ABC
Step: 3
ACD = 30° + x°
Step: 4
50° = 30° + x°
Step: 5
x° = 50° - 30°
Step: 6
x = 20°
Step: 7
Therefore, the measure of x is 20°
Q9What is the measure of the marked exterior angle of the triangle? [Given x = 52° and y = 89°.] A. 37°
B. 144°
C. 141°
D. 91°

Step: 1
In ΔABC, ABC = 52° and BAC = 89°
Step: 2
Since side BC is extended to the point D, exterior angle of ACB is ACD.
Step: 3
The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.
[Exterior angle theorem.]
Step: 4
ABC + BAC = ACD
[From step 3.]
Step: 5
52° + 89° = ACD
[Substitute the values of ABC and BAC.]
Step: 6
ACD = 141°
[Simplify.]
Step: 7
So, the measure of the marked exterior angle of the triangle is 141°.