Drag each angle measure to the correct location on the image. Not all angle measures will be used.
Determine the measures of the angles.
35°
70°
75°
100°
105°
110°

Given:

One internal angle = 75°

External angle = 145°

To find:

The measure of each angle.

Solution:

The reference image is attached below.

The measure of exterior angle is equal to the sum of the measures of the opposite interior angles.

⇒ m∠A + m∠B = ext ∠C

⇒ m∠A + 75° = 145°

Subtract 75° from both sides.

⇒ m∠A + 75° - 75° = 145° - 75°

⇒ m∠A = 70°

Sum of all the angles of a triangle = 180°

⇒ m∠A + m∠B + m∠C = 180°

⇒ 70° + 75° + m∠C = 180°

⇒ 145° + m∠C = 180°

Subtract 145° from both sides.

⇒ 145° + m∠C - 145° = 180° - 145°

⇒ m∠C = 35°

By external angle theorem,

ext∠B = m∠A + m∠C

          = 70° + 35°

ext∠B = 105°

By external angle theorem,

ext∠A = m∠B + m∠C

          = 75° + 35°

ext∠B = 110°