Question

if angle w measures 45°, what are the measures of the other angles in the diagram? use your knowledge of supplementary angles to complete the table. angle measure

Explanation:

Step1: Recall supplementary - angle property

Supplementary angles add up to 180°.

Step2: Find angle adjacent to W

Let the angle adjacent to ∠W be ∠Z. Since ∠W + ∠Z=180° and ∠W = 45°, then ∠Z=180° - 45° = 135°.

Step3: Use vertical - angle property

Vertical angles are equal. ∠W and ∠U are vertical angles, so ∠U = 45°. ∠Z and ∠X are vertical angles, so ∠X = 135°. Also, ∠V and ∠Z are supplementary, so ∠V = 45° (180° - 135°), and ∠Y and ∠W are supplementary, so ∠Y = 135°.

Answer:

∠U = 45°, ∠V = 45°, ∠X = 135°, ∠Y = 135°, ∠Z = 135°