Question

The measure of an angle is seventeen times the measure of a complementary angle. What is the measure of each angle?

Answer 1

First, write an equation system for the problem
For example, x represents the first angle and y represents the second angle
An equation for "the measure of an angle is seventeen times the measure of a complementary angle" is
∴ x = 17y
The sum of complementary angle is 90°. It can be written as
∴ x + y = 90°

Second, use subtitution method to find the value of x and y
Subtitute x with 17y
x + y = 90°
17y + y = 90°
18y = 90°
y = 90°/18
y = 5°

Subtitute y with 5°
x = 17y
x = 17(5)
x = 85°

The measure of each angle is 5° and 85°