Question

The measure of the supplement of an angle exceeds 3 times the measure of the complement of the angle by 10. Find the measure of the complement.

Answer 1

Step-by-step explanation:

• Let the angle be x.

• Let the supplement of the angle = 180 - x

• Let the complement of the angle = 90 - x

Now, According to our assumption we can set up an equation :

➵ (180 - x) - 3(90 - x) = 10

➵ 180 - x - 270 + 3x = 10

➵ 2x - 270 = 10 - 180

➵ 2x - 270 = -170

➵ 2x = -170 + 270

➵ 2x = 100

➵ x = 100/2

➵ x = 50

Therefore,

• The angle = x = 50°

• The supplement of the angle = 180-x = 180 - 50 = 130°

• The complement of the angle = 90 - x = 90 - 50 = 40°