Question

solve for x, y, and z in the figure below.

Explanation:

Step1: Find \(x\) using triangle angle sum

In a triangle, sum of angles is \(180^{\circ}\).
For the left - hand triangle: \(x + 47+ y=180\). First, find \(y\) using the adjacent triangle.

Step2: Find \(y\) using triangle angle sum

For the middle - right triangle: \(y + 58+81 = 180\).

$$y=180-(58 + 81)=180 - 139=41$$

Step3: Find \(x\)

Substitute \(y = 41\) into \(x + 47+y=180\).

$$x=180-(47 + 41)=180 - 88 = 92$$

Step4: Find \(z\) using triangle angle sum

For the right - hand triangle: \(z+58 + 81=180\).

$$z=180-(58 + 81)=180 - 139 = 41$$

Answer:

\(x = 92\), \(y = 41\), \(z = 41\)