Question

The measure of angle A is 4 degrees greater than the measure of angle B. The two angles are complementary. Find the measure for each angle

The measure of angle D is 5 times the measure of angle E. The two angles are supplementary. Find the measure of each angle.

Answer 1

Angle D is 5 times greater than Angle E. These angles is supplementary. This means that their sum is 180°

Answer 2

Given:
Angle A is 4 degrees greater than the measure of Angle B. Both angles are complementary

Complementary angles have a sum of 90°

Angle A = x + 4° ; Angle B = x

x + 4° + x = 90°
2x = 90° - 4°
2x = 86°
x = 86° ÷ 2
x = 43° ANGLE B.

Angle A = x + 4° ⇒ 43° + 4 = 47°

Given:
Angle D is 5 times the measure of Angle E. These angles are supplementary. This means that their sum is 180°

Angle D = 5x ; Angle E = x

5x + x = 180°
6x = 180°
x = 180° ÷ 6
x = 30° Angle E.

Angle D = 5x = 5(30) = 150°