Question

what js the measure of \\( \angle xyz \\)? what is the measure of \\( \angle ywx \\)?

Explanation:

Step1: Calculate ∠XYZ

Use the property of the exterior angle of a triangle.
The exterior angle \(62^{\circ}\) of \(\triangle YWX\) is equal to the sum of the two non - adjacent interior angles (\(12^{\circ}\) and \(\angle XYZ\)).
So, \(\angle XYZ=62^{\circ}- 12^{\circ}\)

$$ \angle XYZ = 50^{\circ} $$

Step2: Calculate ∠YWX

Use the triangle interior angle sum theorem (\(180^{\circ}\)) for \(\triangle YWX\).
First, find \(\angle YXW = 180^{\circ}-62^{\circ}=118^{\circ}\).
Then, \(\angle YWX=180^{\circ}-12^{\circ}-118^{\circ}\)

$$ \angle YWX = 50^{\circ} $$

Answer:

\(\angle XYZ = 50^{\circ}\), \(\angle YWX = 50^{\circ}\)