Question

The measures of two supplementary angles are (2x – 8)° and (3x - 2)°. What is the measure of the

smaller angle?

Answer 1

68°

Explanation:

Here,

• Two supplementary angles are (2x – 8)° and (3x - 2)°.

As we know that the sum of two supplementary angles are 180°. So,

→ (2x – 8)° + (3x – 2)° = 180°

→ 2x° – 8° + 3x° – 2° = 180°

→ 5x° – 10° = 180°

→ 5x° = 180° + 10°

→ 5x° = 190°

→ x = 190° ÷ 5°

→ x = 38°

Supplementary angles are,

• 1st angle = (2x – 8)°

→ 2(38°) – 8

→ (76 – 8)°

→ 68°

• 2nd angle = (3x – 2)°

→ 3(38°) – 2

→ (114 – 2)°

→ 112°

Therefore, the measure of the smaller angle is 68°.