Question

find the measure of the missing angles.

Explanation:

Step1: Find the measure of \(x\)

Since \(x\) and the \(24^{\circ}\) angle are complementary (they form a right - angle, \(90^{\circ}\)).
\(x = 90^{\circ}-24^{\circ}\)
\(x = 66^{\circ}\)

Step2: Find the measure of \(y\)

Since \(y\) and \(x\) are supplementary (they form a straight - angle, \(180^{\circ}\)).
\(y=180^{\circ}-x\)
Substitute \(x = 66^{\circ}\) into the equation:
\(y = 180^{\circ}-66^{\circ}\)
\(y = 114^{\circ}\)

Answer:

\(x = 66^{\circ}\), \(y = 114^{\circ}\)