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Chapter 5: Q. 214 (page 645)

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

The difference of two complementary angles is 17 degrees. Find the measures of the angles.

Short Answer

Expert verified

The measures of angles are 36.5and53.5degrees.

Step by step solution

01

Step 1. Given Information   

The given data is that the difference of the two complementary angles is 17 degrees.

02

Step 2. Calculation  

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

Difference of the two complementary angles is 17 degrees that isx-y=17掳--(1)

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

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

x-y+x+y=17掳+90掳2x=107掳x=53.5掳

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

x+y=90掳y=90掳-53.5掳y=36.5掳

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