CONSECUTIVE EXTERIOR ANGLES WORKSHEET

Problem 1 :

In the figure shown below, m∠1 = 105°. Find the measure of ∠8.

Problem 2 :

In the figure shown below, m∠1 = 102°. Find the measures ∠8, ∠15 and ∠10.

Problem 3 :

In the figure shown below, lines m and n are parallel and p is transversal. Find the value of x.

Problem 4 :

In the figure shown below, solve for x.

1. Answer :

In the figure above, lines m and n are parallel and p is transversal.

By Theorem, ∠1 and ∠8 are supplementary.

m∠1 + m∠8  =  180°

Substitute m∠1 = 105°. 

105° + m∠8  =  180°

Subtract 105° from each side. 

m∠8  =  75°

2. Answer :

In the figure above, lines m and n are parallel, p and q are parallel.

By Theorem, ∠1 and ∠8 are supplementary.

m∠1 + m∠8  =  180°

Substitute m∠1 = 102°. 

102° + m∠8  =  180°

Subtract 102° from each side. 

m∠8  =  78°

By Theorem, ∠1 and ∠10 are supplementary.

m∠1 + m∠10  =  180°

Substitute m∠1 = 102°. 

102° + m∠10  =  180°

Subtract 102° from each side. 

m∠10  =  78°

By Theorem, ∠10 and ∠15 are supplementary.

m∠10 + m∠15  =  180°

Substitute m∠10 = 78°. 

78° + m∠15  =  180°

Subtract 78° from each side. 

m∠15  =  102°

Therefore, 

m∠8  =  78°

m∠10  =  78°

m∠15  =  102°

3. Answer :

In the figure above, lines m and n are parallel and p is transversal.

By Theorem, (3x + 28)° and 5x° are supplementary.

(3x + 28)° + 5x°  =  180°

3x + 28 + 5x  =  180

8x + 28  =  180

Subtract 28 from each side. 

8x  =  152

Divide each side by 8.

x  =  19

4. Answer :

In the figure above, by Theorem, y° and 74° are supplementary angles. 

y° + 74°  =  180°

Subtract 74° from each side. 

y°  =  106°

(4x + 6)° and y° are corresponding angles. 

(4x + 6)°  =  y°

Substitute y° = 106°.  

(4x + 6)°  =  106°

4x + 6  =  106

Substract 6 from each side. 

4x  =  100

Divide each side by 4. 

x  =  25

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