Question

an angle measures 134° more than the measure of its supplementary angle. what is 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 \(x + 134\). Since supplementary angles sum to \(180^{\circ}\), we have the equation \(x+(x + 134)=180\).

Step2: Simplify the equation

Combine like - terms: \(2x+134 = 180\).
Subtract \(134\) from both sides: \(2x=180 - 134\), so \(2x = 46\).

Step3: Solve for \(x\)

Divide both sides by \(2\): \(x=\frac{46}{2}=23\).

Step4: Find the other angle

The other angle is \(x + 134\). Substitute \(x = 23\) into it, we get \(23+134 = 157\).

Answer:

\(23^{\circ}\) and \(157^{\circ}\)