Question

1. find the values of x, y, and z. 13 34° 6 81° y

Explanation:

Step1: Find the value of x

Use the angle - sum property of a triangle. The sum of interior angles of a triangle is 180°. In the left - hand triangle, we have \(x + 34+ (180 - 81)=180\). First, simplify the equation: \(x+34 + 99 = 180\), then \(x+133 = 180\), and \(x=180 - 133=47\).

Step2: Find the value of y

The angle with measure \(y\) and the angle with measure 81° are vertical angles. Vertical angles are equal. So \(y = 81\).

Step3: Find the value of z

Use the angle - sum property of a triangle for the right - hand triangle. We know one angle is \(y = 81^{\circ}\) and assume the third angle in the right - hand triangle is \(a\). The angle adjacent to \(a\) in the left - hand triangle is \(180 - 81=99^{\circ}\). In the right - hand triangle, \(z+81+(180 - 99)=180\). Simplify the equation: \(z + 81+81 = 180\), \(z+162 = 180\), so \(z=180 - 162 = 18\).

Answer:

\(x = 47\), \(y = 81\), \(z = 18\)