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Chapter 5: Q. 213 (page 645)

In the following exercises, translate to a system of equations and solve.

The difference of two complementary angles is 55 degrees. Find the measures of the angles.

Short Answer

Expert verified

The measures of angles are 17.5and72.5degrees.

Step by step solution

01

Step 1. Given Information  

The given data is that the difference of the two complementary angles is 55 degrees.

02

Step 2. Calculation  

Let x be the first angle and y be the second angle.

Difference of the two complementary angles is 88 degrees that is x-y=55°--(1)

Also, the angles are complementary that is x+y=90°--(2)

Add equations (1) and (2) and solve.

x-y+x+y=55°+90°2x=145°x=72.5°

Substitute the value of x in equation (2) to find the value of y.

x+y=90°y=90°-72.5°y=17.5°

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