Question

question
find the measure of the missing angles.
answer attempt 2 out of 2
$x = square^{circ}$ $y = square^{circ}$

Explanation:

Step1: Use right - angle property

We know that a right - angle is 90°. Since the angle composed of the 30° angle and \(x\) is a right - angle, we have \(x + 30^{\circ}=90^{\circ}\).

Step2: Solve for \(x\)

Subtract 30° from both sides of the equation \(x + 30^{\circ}=90^{\circ}\), so \(x=90^{\circ}- 30^{\circ}=60^{\circ}\).

Step3: Use straight - angle property

A straight - angle is 180°. The angle composed of \(x\) and \(y\) is a straight - angle, so \(x + y=180^{\circ}-90^{\circ}\) (because there is a right - angle in the straight - angle). Since \(x = 60^{\circ}\), and \(x + y=90^{\circ}\) (the non - right part of the straight - angle).

Step4: Solve for \(y\)

Substitute \(x = 60^{\circ}\) into \(x + y=90^{\circ}\), we get \(y=90^{\circ}-x\). Then \(y = 90^{\circ}-60^{\circ}=30^{\circ}\).

Answer:

\(x = 60\)
\(y = 30\)