Question

question 3
find the unknown angle measures.
drawing is not to scale.
$x = square^circ$
$y = square^circ$
$w = square^circ$

Explanation:

Step1: Find \(x\)

Use the triangle angle - sum theorem (\(180^{\circ}\) in a triangle).
For the left - hand triangle (with angles \(50^{\circ}\), \(94^{\circ}\), and the angle adjacent to \(x\)):
The third angle of this triangle is \(180-(50 + 94)=180 - 144=36^{\circ}\).
Then, for the triangle with angles \(31^{\circ}\), \(36^{\circ}\), and \(x\):
\(x=180-(31 + 36)=180-67 = 113\).

Step2: Find \(y\)

\(y\) and \(x\) are supplementary (linear pair).
\(y = 180 - x\). Since \(x = 113\), then \(y=180 - 113=67\).

Step3: Find \(w\)

Use the triangle angle - sum theorem for the right - hand triangle (with angles \(109^{\circ}\), \(y = 67^{\circ}\), and \(w\)).
\(w=180-(109 + 67)=180 - 176=4\).

Answer:

\(x = 113\), \(y = 67\), \(w = 4\)