Question

find the unknown angle measures. drawing is not to scale. $x = square$ degrees $y = square$ degrees $w = square$ degrees question help: message instructor

Explanation:

Step1: Find the third - angle of the first triangle

The sum of angles in a triangle is 180°. For the first triangle with angles 86° and 53°, the third - angle is $180-(86 + 53)=41$ degrees.

Step2: Use the vertical - angles property

The angle vertical to $x$ has an angle measure that can be found from the first triangle. The angle adjacent to the 41 - degree angle in the overlapping part forms a linear pair. The angle adjacent to 41° is $180 - 41=139$ degrees. Then, since vertical angles are equal, $x$ is equal to the non - adjacent angle in the small triangle formed by the intersection. Using the angle - sum property of a triangle in the small triangle with one angle 32°, we know that $x=180-(32 + 41)=107$ degrees.

Step3: Find angle $y$

In the small triangle where one angle is 32° and the angle opposite to $x$ (which is also 107°), then $y = 180-(107+32)=41$ degrees.

Step4: Find angle $w$

For the second triangle with an exterior angle of 130°. The non - adjacent interior angles of this exterior angle are $y$ and $w$. Since an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles, $w=130 - 41 = 89$ degrees.

Answer:

$x = 107$ degrees
$y = 41$ degrees
$w = 89$ degrees