Question

find the measure of the missing angles. answer attempt 1 out of 2 x = y =

Explanation:

Step1: Use complementary - angle property

Since the angle next to \(x\) and the \(53^{\circ}\) angle are complementary (sum to \(90^{\circ}\)), we have \(x + 53^{\circ}=90^{\circ}\).
So, \(x=90^{\circ}-53^{\circ}\).

Step2: Calculate the value of \(x\)

\(x = 37^{\circ}\)

Step3: Use supplementary - angle property

The angle \(y\) and the \(53^{\circ}+x\) angle are supplementary (sum to \(180^{\circ}\)). First, we know \(x = 37^{\circ}\), so the angle composed of \(x\) and \(53^{\circ}\) is \(37^{\circ}+53^{\circ}=90^{\circ}\). Then \(y+90^{\circ}=180^{\circ}\), so \(y = 180^{\circ}-90^{\circ}\).

Step4: Calculate the value of \(y\)

\(y = 90^{\circ}\)

Answer:

\(x = 37^{\circ}\), \(y = 90^{\circ}\)