Question

1. 34° 29° 61° x y z z = ____

Explanation:

Step1: Use angle - sum property of a triangle

In the left - hand triangle, the sum of interior angles of a triangle is 180°. Let's find the third angle of the left - hand triangle. Let the third angle be \(a\). Then \(a=180-(34 + 61)=85^{\circ}\).

Step2: Find angle \(x\)

Since the straight - line has an angle of 180°, and the angle adjacent to \(x\) in the left - hand triangle is 85°, then \(x = 180 - 85=95^{\circ}\).

Step3: Use angle - sum property for the right - hand triangle

In the right - hand triangle, we know one angle is 29° and we want to find \(y\) and \(z\). First, note that the angle opposite to the 61° angle in the large triangle is also 61° (vertically opposite angles).
For the right - hand triangle, using the angle - sum property of a triangle (\(180^{\circ}\) for the sum of interior angles), if we consider the right - hand triangle with angles 29°, \(y\), and 61°. Then \(y=180-(29 + 61)=90^{\circ}\).

Step4: Find angle \(z\)

We already know from the vertical - angle property that \(z = 61^{\circ}\).

Answer:

\(x = 95^{\circ}\), \(y = 90^{\circ}\), \(z = 61^{\circ}\)