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Chapter 5: Q. 5.78 (page 635)

Translate to a system of equations and then solve:

The difference of two complementary angles is 80 degrees. Find the measures of the angles

Short Answer

Expert verified

The angle measures are 85 degrees and 5 degrees

Step by step solution

01

Given Information 

The difference of two complementary angles is 80 degrees.

02

Assume variables

Let 'x be the measure first angle and 'y' be the measure of second angle

The sum of complementary angles is equal to 90 degree

x + y =90

The difference of two complementary angles is 80 degrees.

x - y = 80

03

Solve for x  and y 

x+y=90x-y=80------2x=170Dividebothsidesby2x=85x+y=9085+y=90y=90-85y=5

The angle measures are 85 degrees and 5 degrees

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