Question

13. The measure of the supplement of angle A is 40 degrees greater than twice the measure of the complement of angle of A. What is the sum in degrees, of the measures of the supplement and complement of angle A?

Answer 1

Given:

• The measure of the supplement of angle A is 40 degrees greater than twice the measure of the complement of angle of A

To Find:

• What is the sum in degrees, of the measures of the supplement and complement of angle A?

Solution:

Let angles x be the measure of angle A l.

• Supplement of angle A = 180° - x
• Complement of angle A = 90° - x

According to Question:

➝ 180 - x = 2 (90 - x) + 40

➝ 180 - x = 180 - 2x + 40

➝ - x = - 2x + 40

➝ x = 40

Then, supplement of angle A is

➝ 180 -x

➝ 180 - 40

➝ 140°

Complement of angle A is

➝ 90 - x

➝ 90 - 40

➝ 50°

The sum of supplement and complement of angle A is

➝ 140 + 50

➝ 190°

Hence,

• The sum of supplement and complement of angle is 190°

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