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Chapter 4: Q 99. (page 405)

Two angles are complementary. The measure of the larger angle is ten more than four times the measure of the smaller angle. Find the measures of both angles.

Short Answer

Expert verified

The measures of angles are 74and16

Step by step solution

01

Step 1. Given information

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=90

02

Step 2. Creating the equation 

The measures of the larger angle is ten more than four times the measure of the smaller angle.

Therefore,x=10+4y

03

Step 3. Finding the value y

Substitute the value of x=10+4yin the equation

Therefore,

10+4y+y=90

10+5y=90

5y=80

y=805

=16

04

Step 4. Finding the value x

Put, y=16into x=10+4yand solve for x

x=10+4yx=10+4(16)

=10+64

=74

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