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Chapter 4: Q. 98 (page 405)

Two angles are complementary. The measure of the larger angle is twelve less than twice the measure of the smaller angle. Find the measures of both the angles.

Short Answer

Expert verified

The measures of angles are 56and34

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=90

02

Step 2. Creating the equation

The measures of the larger angle is twelve less than twice the measure of the smaller angle.

Therefore,x=2y-12

03

Step 3. Finding the value y

Substitute the value of x=2y-12in the equation x+y=90

Therefore,

x+y=90

2y-12+y=90

3y-12=90

3y=90+12

3y=102

y=1023

=34

04

Step 4. Finding the value x

Put, y=34into x=2y-12and solve for x

x=2y-12x=2(34)-12

=68-12=56

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