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Chapter 4: Q 4.33 (page 394)

Translate to a system of equations and then solve:

The difference of two complementary angles is 20degrees. Find the measures of the angles.

Short Answer

Expert verified

The measure of angles are 55鈭�and 35鈭�.

Step by step solution

01

Step 1. Given

We are given that the difference between two complementary angles is 20鈭�.

02

Step 2. Formation of equations.

We know that the sum of complementary angles is equal to 90鈭�.

Let the one angle be x, and the other angle will be y.

So, as per the given statement the equation will be,

x+y=90鈭�

y=90鈭�-x

localid="1644599820429" x-y=20鈭�x-(90鈭�-x)=20鈭�x-90鈭�+x=20鈭�2x-90鈭�=20鈭�2x=20鈭�+90鈭�2x=110鈭�

Dividing by 2, we get

x=55鈭�

And the other angle will be90鈭�-55鈭�=35鈭�

03

Step 4. Checking the solution  

Checking the solution by putting the value of x,yin the equations, we get

x+y=90鈭�55鈭�+35鈭�=90鈭�90鈭�=90鈭�x-y=20鈭�55鈭�-35鈭�=20鈭�20鈭�=20鈭�

This is true, hence the solution is correct.

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