Question

find the value of each variable in the figure on the right. x = 72 (simplify your answer.) y = (simplify your answer.)

Explanation:

Step1: Use angle - sum property of a triangle

The sum of interior angles of a triangle is 180°. In the triangle with angles 34°, 74° and the third - angle (let's call it z), we have z=180°-(34° + 74°).
z = 180-(34 + 74)=180 - 108=72°.

Step2: Use vertical - angle property

Vertical angles are equal. Angle x is a vertical angle to the 72° angle in the triangle. So x = 72°.

Step3: Use linear - pair property

Angles x and y form a linear pair. A linear pair of angles sums to 180°. So y=180 - x. Since x = 72°, then y = 180-72 = 108°.

Answer:

y = 108