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°