Question

find the measure of the missing angles.
answer attempt 1 out of 2
$x = square ^ { circ }$
$y = square ^ { circ }$

Explanation:

Step1: Find the value of \(x\)

Since \(x\) and \(36^{\circ}\) are complementary angles (they form a right - angle, \(90^{\circ}\)).
\(x + 36^{\circ}=90^{\circ}\)
\(x=90^{\circ}-36^{\circ}\)
\(x = 54^{\circ}\)

Step2: Find the value of \(y\)

The sum of angles around a point on a straight line is \(180^{\circ}\). One of the angles on the straight line is \(90^{\circ}\) (right - angle) and \(x = 54^{\circ}\).
\(y+90^{\circ}+x=180^{\circ}\)
Substitute \(x = 54^{\circ}\) into the equation:
\(y+90^{\circ}+54^{\circ}=180^{\circ}\)
\(y+144^{\circ}=180^{\circ}\)
\(y=180^{\circ}-144^{\circ}\)
\(y = 36^{\circ}\)

Answer:

\(x = 54\), \(y = 36\)