ALTERNATE EXTERIOR ANGLES WORKSHEET

Problem 1 :

In the figure shown below, m∠8 = 75°. Find m∠1.

Problem 2 :

In the figure shown below, m∠2 = 78°. Find the measures of ∠8, ∠10 and ∠16.

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, ∠7 and ∠8 form a linear pair. 

m∠7 + m∠8 = 180°

Substitute m∠8 = 75°. 

m∠7 + 75° = 180°

Subtract 75° from each side. 

m∠7 = 105°

∠1 and ∠7 are alternate exterior angles.

∠1 ≅ ∠7

m∠1 = m∠7

Substitute m∠7 = 105°.

m∠1 = 105°

2. Answer :

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

∠2 and ∠8 are alternate exterior angles. 

∠2 ≅ ∠8

m∠2 = m∠8

Substitute m∠2 = 78°.

78° = m∠8

∠8 and ∠16 are corresponding angles. 

∠8 ≅ ∠16

m∠8 = m∠16

Substitute m∠8 = 78°. 

78° = m∠16

∠10 and ∠16 are alternate interior angles. 

∠10 ≅ ∠16

m∠10 = m∠16

Substitute m∠16 = 78°. 

m∠10 = 78°

Therefore, 

m∠8 = 78°

m∠10 = 78°

m∠16 = 78°

3. Answer :

In the figure above m and n are parallel and p is transversal. Angles 5x° and (3x + 28)° are alternate exterior angles and they are congruent. 

By the definition of congruent angles, 

5x° = (3x + 28)°

5x = 3x + 28

Subtract 3x from each side. 

2x = 28

Divide each side by 2.

x = 14

4. Answer :

In the figure above, y° and 74° are alternate exterior angles and they are equal.

y° = 74°

(4x + 6)° and y° are alternate exterior angles and they are equal.

(4x + 6)° = y°

Substitute y° = 74°.

(4x + 6)° = 74°

4x + 6 = 74

Subtract 6 from each side. 

4x = 68

Divide each side by 4.

x = 17

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