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 \(x\)

Vertical angles are equal. Since \(x\) and \(41^{\circ}\) are vertical angles, \(x = 41^{\circ}\).

Step2: Find the value of \(y\)

A full - circle around a point is \(360^{\circ}\). There is a right - angle (\(90^{\circ}\)) in the figure. Using the angle - sum property: \(y+90^{\circ}+41^{\circ}+x = 360^{\circ}\). But since \(x = 41^{\circ}\), we can also use the fact that \(y\) and \(41^{\circ}\) are supplementary with the right - angle. \(y=360^{\circ}-90^{\circ}-41^{\circ}-41^{\circ}=139^{\circ}\) (another way: \(y = 90^{\circ}+49^{\circ}=139^{\circ}\) as the sum of angles on a line).

Answer:

\(x = 41\), \(y = 139\)