Question

13 select the correct answer from each drop - down menu. in the figure, x = , y = , and z = . reset next

Explanation:

Step1: Find angle x using angle - sum property of a triangle

The sum of interior angles of a triangle is 180°. In the left - hand triangle, the third interior angle is \(180^{\circ}-(45^{\circ}+50^{\circ}) = 85^{\circ}\). Angle x and this interior angle are supplementary (linear pair), so \(x = 180^{\circ}-85^{\circ}=95^{\circ}\).

Step2: Find angle y using angle - sum property of a triangle

In the right - hand triangle, one interior angle is \(52^{\circ}\) and the other non - y interior angle is part of the linear pair with the \(50^{\circ}\) angle from the left - hand triangle. So the second interior angle of the right - hand triangle is \(180 - 50=130^{\circ}\). Then, using the angle - sum property of a triangle (\(180^{\circ}\) for the sum of interior angles), the third interior angle of the right - hand triangle is \(180-(130 + 52)= - 2^{\circ}\), which is wrong. Let's use another approach. Angle y and the non - \(50^{\circ}\) non - \(52^{\circ}\) angle of the right - hand triangle are supplementary. First, find the non - \(50^{\circ}\) non - \(52^{\circ}\) angle of the right - hand triangle. The sum of angles in the left - hand triangle gives the third angle as \(85^{\circ}\). The angle adjacent to y in the right - hand triangle is \(180-(85 + 52)=43^{\circ}\), so \(y = 180 - 43=137^{\circ}\).

Step3: Find angle z

Angle z and the \(52^{\circ}\) angle are supplementary (linear pair), so \(z=180 - 52 = 128^{\circ}\).

Answer:

\(x = 95^{\circ}\), \(y = 137^{\circ}\), \(z = 128^{\circ}\)