Question

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

Explanation:

Step1: Find the value of \(x\)

We know that the sum of angles in a right - angle is \(90^{\circ}\). Given one angle is \(60^{\circ}\), so \(x + 60^{\circ}=90^{\circ}\).
Subtracting \(60^{\circ}\) from both sides, we get \(x=90^{\circ}-60^{\circ}\).

Step2: Find the value of \(y\)

We know that the sum of angles around a point on a straight line is \(180^{\circ}\). One of the angles is \(90^{\circ}\) (right - angle) and we found \(x = 30^{\circ}\). So \(y+x + 90^{\circ}=180^{\circ}\).
Substituting \(x = 30^{\circ}\) into the equation: \(y+30^{\circ}+90^{\circ}=180^{\circ}\).
First, simplify the left - hand side: \(y + 120^{\circ}=180^{\circ}\).
Then subtract \(120^{\circ}\) from both sides: \(y=180^{\circ}-120^{\circ}\).

Answer:

\(x = 30^{\circ}\), \(y = 60^{\circ}\)