Question

1. determine the measures of the unknown angles in the figure.

Explanation:

Step1: Use angle - sum property of a triangle

The sum of interior angles of a triangle is 180°. For the right - hand triangle, we have \(47^{\circ}+63^{\circ}+z = 180^{\circ}\), where \(z\) is the third angle. So \(z=180-(47 + 63)=70^{\circ}\).

Step2: Use vertical - angles property

The angle \(x\) and the angle \(z\) (from Step 1) are vertical angles. Vertical angles are equal. So \(x = 70^{\circ}\).

Step3: Use angle - sum property for left - hand triangle

For the left - hand triangle, we know that \(y + y+x=180^{\circ}\). Substitute \(x = 70^{\circ}\) into the equation: \(2y+70 = 180\). Then \(2y=180 - 70=110\), and \(y = 55^{\circ}\).

Answer:

\(x = 70^{\circ}\), \(y = 55^{\circ}\)