EDGE Math 8

Example

The measure of the complement of an angle is 2° more than thrice its measure. What is the measure of each angle?

Solution

Let x = the measure of the angle, and $3 x + 2$ = the measure of its complement.

The sum of the measures of two complementary angles is 90° and so you form the equation

x + (3 x + 2) = 90.

Solving the equation, you will get:

$4 x + 2$	$= 90$	Combine similar terms
$4 x + 2 - 2$	$= 90 - 2$	Subtraction property of equality
$4 x$	$= 88$	Combine similar terms.
$\frac{4 x}{4}$	$= \frac{88}{4}$	Division property of equality
$x$	$= 22.$

Hence, the measure of the angle is 22° and the measure of its complement is

3 x + 2 = 3 (22) + 2 = 68 ° .