Question

A pair of angles is supplementary if the sum of their measures is 180 degrees. A pair of angels is complementary if the sum of their measures 90 degrees. the supplement of a given angel is 10 degrees more than twice its complement. Let 90-x equal the degree measure of its complement and 180-x equal the degree measure of its supplement. Write and solve an equation to find the measure of the given angel.

Answer 1

Answer:

The measure of the complement =

= 80°

The measure of the supplement=

= 170°

Step-by-step explanation:

Let

90-x equal the degree measure of its complement

180-x equal the degree measure of its supplement.

We are told in the question that: the supplement of a given angle is 10 degrees more than twice its complement.

Hence, the Equation is;

(180 - x) = 10° + 2(90 - x)

180 - x = 10 + 180 - 2x

Collect like terms

-x + 2x = 10 + 180 - 180

x = 10°

Hence,

The measure of the complement =

90 - x

= 90 - 10

= 80°

The measure of the supplement=

180 - x

= 180 - 10

= 170°