PROBLEMS INVOLVING EXTERIOR ANGLES OF A TRIANGLE

In each case, solve for a°.

Problem 1 :

Solution :

Exterior angle = 125°.

Remote interior angles are 70° and a°.

Exterior angle = Sum of two remote interior angles

125° = 70° + a°

Subtract 70° from both sides.

55° = a°

Problem 2 :

Solution :

Exterior angle = a°.

Remote interior angles are 90° and 35°.

Exterior angle = Sum of two remote interior angles

a° = 90° + 35°

a° = 125°

Problem 3 :

Solution :

Exterior angle = a°. 

Remote interior angles are 45° and 101°.

Exterior angle = Sum of two remote interior angles

a° = 45° + 101°

a° = 146°

Problem 4 :

Solution :

Exterior angle = 132°.

Remote interior angles are a° and 63°.

Exterior angle = Sum of two remote interior angles

132° = a° + 63°

Subtract 63° from both sides.

69° = a°

Problem 5 :

Solution :

Exterior angle = 117°.

Remote interior angles are a° and 62°.

Exterior angle = Sum of two remote interior angles

117 = a° + 62°

Subtract 62° from both sides.

55° = a°

Problem 6 :

Solution :

Exterior angle = a°.

Remote interior angles are 90° and 40°.

Exterior angle = Sum of two remote interior angles

a° = 90° + 40°

a = 130°

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