Question

find the value of each variable in the figure on the right. x = 85 (simplify your answer.) y = (simplify your answer.)

Explanation:

Step1: Use triangle - angle - sum property

The sum of interior angles of a triangle is 180°. In the given triangle, we have \(29^{\circ}+66^{\circ}+x = 180^{\circ}\).
So, \(x=180-(29 + 66)=180 - 95=85\).

Step2: Use linear - pair property

The angle \(y\) and the angle adjacent to it (which is \(x = 85^{\circ}\)) form a linear - pair. A linear - pair of angles sums to 180°. So, \(y=180 - x\). Since \(x = 85^{\circ}\), then \(y=180 - 85=95\).

Answer:

\(x = 85\), \(y=95\)