Question

the measure of the supplement of an angle is 60° less than four times the measure of the complement of the angle. find the measure of the angle.

Explanation:

Step1: Define the angle

Let the measure of the angle be \( x \) degrees.

Step2: Find complement and supplement

The complement of the angle is \( (90 - x)^\circ \) (since complementary angles add up to \( 90^\circ \)).
The supplement of the angle is \( (180 - x)^\circ \) (since supplementary angles add up to \( 180^\circ \)).

Step3: Set up the equation

The problem states that the supplement is \( 60^\circ \) less than four times the complement. So we can write the equation:
\( 180 - x = 4(90 - x) - 60 \)

Step4: Solve the equation

First, expand the right - hand side:
\( 180 - x = 360 - 4x - 60 \)
Simplify the right - hand side:
\( 180 - x = 300 - 4x \)
Add \( 4x \) to both sides:
\( 180 - x+4x = 300 - 4x + 4x \)
\( 180 + 3x = 300 \)
Subtract 180 from both sides:
\( 3x=300 - 180 \)
\( 3x = 120 \)
Divide both sides by 3:
\( x=\frac{120}{3}=40 \)

Answer:

\( 40 \)