Question

find the measure of the missing angles.
answer attempt 2 out of 3
$x=square^{circ}$ $y=square^{circ}$
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Explanation:

Step1: Find the value of \( x \)

Since the sum of angles in a right - angle relation ( \( 90^{\circ}\) ) with \( 31^{\circ}\), we use \( x+31^{\circ}=90^{\circ}\).
Subtracting \( 31^{\circ}\) from both sides: \( x = 90^{\circ}-31^{\circ}\).

Step2: Find the value of \( y \)

We know that \( y\) and \( x + 31^{\circ}\) are vertical angles. First, \( x+31^{\circ}=90^{\circ}\). Also, \( y\) and \( 31^{\circ}\) and the right - angle (\(90^{\circ}\)) are related as \( y+31^{\circ}+90^{\circ}=180^{\circ}\) (sum of angles on a straight line). Another way: Since \( y\) and \( x + 31^{\circ}\) are vertical angles, and \( x = 59^{\circ}\), \( y=x + 31^{\circ}+90^{\circ}-90^{\circ}\) (using the property of vertical angles). Or using the property that \( y\) and \( 59^{\circ}\) (value of \( x\)) are supplementary (because of the straight - line angle property). \( y=180^{\circ}-59^{\circ}\).

Answer:

\( x = 59^{\circ}\), \( y = 121^{\circ}\)