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Chapter 4: Q. 96 (page 405)

Translate to a system of equation and solve.

The difference of two complementary angles is 55degrees. Find the measures of the angles.

Short Answer

Expert verified

The measures of angles are 75.5and17.5

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

Thereforex+y=90

02

Step 2. Creating the equation

The difference of two angles is 55.

Therefore,x-y=55

03

Step 3. Finding the value x

x+y=90..........(1)

x-y=55...........(2)

Solve for x:

x+y=90x-y=55

2x =145

x=1452

=75.5

04

Step 4. Finding the value y

Substitute x=75.5, in the equation x+y=90

Therefore,

75.5+y=90

y=90-75.2

=17.5

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