Question

an angle measures 86.6° 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 \(x\). Then the measure of the other angle is \(x + 86.6\). Since supplementary angles sum to \(180^{\circ}\), we have \(x+(x + 86.6)=180\).

Step2: Simplify the equation

Combine like terms: \(2x+86.6 = 180\).
Subtract \(86.6\) from both sides: \(2x=180 - 86.6\), so \(2x = 93.4\).

Step3: Solve for \(x\)

Divide both sides by \(2\): \(x=\frac{93.4}{2}=46.7\).

Step4: Find the other angle

The other angle is \(x + 86.6=46.7+86.6 = 133.3\).

Answer:

\(46.7\) and \(133.3\)