Question

an angle measures 6° more than the measure of its supplementary angle. what is the measure of each angle? ° and °

Explanation:

Step1: Set up the equation

Let the measure of the supplementary angle be \(x\) degrees. Then the measure of the other angle is \(x + 6\) degrees. Since supplementary angles add up to \(180^{\circ}\), we have the equation \(x+(x + 6)=180\).

Step2: Simplify the equation

Combine like - terms: \(2x+6 = 180\).
Subtract 6 from both sides: \(2x=180 - 6\), so \(2x=174\).

Step3: Solve for \(x\)

Divide both sides by 2: \(x=\frac{174}{2}=87\).

Step4: Find the measure of the other angle

The other angle is \(x + 6\). Substitute \(x = 87\) into \(x + 6\), we get \(87+6 = 93\).

Answer:

\(87\) and \(93\)