Question

an angle measures 114° 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 \(x + 114\). Since supplementary angles sum to \(180^{\circ}\), we have \(x+(x + 114)=180\).

Step2: Simplify the equation

Combine like - terms: \(2x+114 = 180\).
Subtract \(114\) from both sides: \(2x=180 - 114\), so \(2x = 66\).

Step3: Solve for \(x\)

Divide both sides by \(2\): \(x=\frac{66}{2}=33\).

Step4: Find the other angle

The other angle is \(x + 114\). Substitute \(x = 33\) into it, we get \(33+114 = 147\).

Answer:

\(33\) and \(147\)