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Chapter 4: Q. 103 (page 405)

Two angles are supplementary. The measure of the larger angle is five less than four times the measure of the smaller angle. Find the measure of both angles.

Short Answer

Expert verified

The measures of angle are143and37.

Step by step solution

01

Step 1. Given information

Suppose xrepresents the measure of the first angle.

and similarly, yrepresents the measure of the second angle

Now, both the angles are complementary

Therefore,

x+y=180

02

Step 2. Creating the equation 

The measures of the larger angle is five less than four times the measure of the smaller angle.

Therefore,x=4y-5

03

Step 3. Finding the value y

Substitute the value of x=4y-5in the equation x+y=180

Therefore,

x+y=180

4y-5+y=180

5y-5=180

5y=180+5

5y=185

y=1855

=37

04

Step 4. Finding the value 

Put, y=37into x=4y-5and solve for x

x=4y-5

=148-5=143

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