Question

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

Explanation:

Step1: Find \(x\)

In the left - hand triangle, using the angle - sum property of a triangle (\(180^{\circ}\) in a triangle).
The third angle in the left - hand triangle (excluding \(40^{\circ}\) and \(90^{\circ}\)) is \(180-(40 + 90)=50^{\circ}\).
Then, for the small triangle with angles \(20^{\circ}\), \(x\) and the angle we just found (\(50^{\circ}\)), using the angle - sum property of a triangle (\(x+20 + 50=180\)).
\(x=180-(20 + 50)=110\)

Step2: Find \(y\)

Since \(x\) and \(y\) are supplementary angles (\(x + y=180\)).
\(y=180 - x\). Substitute \(x = 110\), so \(y=70\)

Step3: Find \(w\)

In the right - hand triangle, using the angle - sum property of a triangle (\(180^{\circ}\) in a triangle).
\(w+125 + y=180\). Substitute \(y = 70\)
\(w=180-(125 + 70)=180 - 195+ 20=25\)

Answer:

\(x = 110\), \(y = 70\), \(w = 25\)