Question

an angle measures 71.6° more than the measure of its supplementary angle. what is the measure of each angle?
° and
°
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Explanation:

Step1: Set up the equation

Let the measure of the supplementary angle be \(x\). Then the measure of the given angle is \(x + 71.6\). Since supplementary angles sum to \(180^{\circ}\), we have the equation \(x+(x + 71.6)=180\).

Step2: Simplify the equation

Combine like - terms: \(2x+71.6 = 180\).
Subtract \(71.6\) from both sides: \(2x=180 - 71.6\), so \(2x = 108.4\).

Step3: Solve for \(x\)

Divide both sides by \(2\): \(x=\frac{108.4}{2}=54.2\).

Step4: Find the measure of the other angle

The other angle is \(x + 71.6\). Substitute \(x = 54.2\) into it: \(54.2+71.6 = 125.8\).

Answer:

\(54.2\) and \(125.8\)