ALTERNATE INTERIOR ANGLES WORKSHEET

Problem 1 :

In the figure shown below, m∠8 = 75°. Find m∠3.

Problem 2 :

In the figure shown below, m∠3 = 102°. Find the measures ∠5, ∠11 and ∠13.

Problem 3 :

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

Problem 4 :

Using a 3^rd parallel Line – Auxiliary Line, find the value of x.

1. Answer :

In the figure above, lines m and n are parallel, ∠5 and ∠8 form a linear pair. 

m∠5 + m∠8  =  180°

Substitute m∠8 = 75°. 

m∠5 + 75°  =  180°

Subtract 75° from each side. 

m∠5  =  105°

∠3 and ∠5 are alternate interior angles.

∠3 ≅ ∠5

m∠3  =  m∠5

Substitute m∠5 = 105°.

m∠3  =  105°

2. Answer :

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

∠3 and ∠5 are alternate interior angles. 

∠3 ≅ ∠5

m∠3  =  m∠5

Substitute m∠3 = 102°.

102°  =  m∠5

∠5 and ∠13 are corresponding angles. 

∠5 ≅ ∠13

m∠5  =  m∠13

Substitute m∠5 = 102°. 

102°  =  m∠13

∠11 and ∠13 are alternate interior angles. 

∠11 ≅ ∠13

m∠11  =  m∠13

Substitute m∠13 = 102°. 

m∠11  =  102°

Therefore, 

m∠5  =  102°

m∠11  =  102°

m∠13  =  102°

3. Answer :

In the figure above, lines m and n are parallel and p is transversal. Then, the angles 5x° and (3x + 28)° are alternate interior 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, a° and 118° are alternate interior angles and they are equal.

a°  =  118°

b° and 144° are alternate interior angles and they are equal.

b°  =  144°

In the figure above, 

x  =  a + b

=  118 + 144

=  262

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