Question

Given that the measure of X is 57° and the measure of y is 51° find the measure of z 

Answer 1

9514 1404 393

Answer:

  132°

Step-by-step explanation:

Name the vertex of each angle the same as the angle letter. Name the intersection of the "horizontal" and "vertical lines" point Q.

Angle ZXQ is vertical to ∠x, so is the same measure.

Angle YQX is the value that makes the sum of angles in triangle XYQ be 180°. That is ...

  ∠YQX = 180° -51° -57° = 72°

This is also the measure of its vertical angle in the other triangle. Angle z is the sum of that vertical angle and 60°, so we have ...

  ∠z = 72° +60°

  ∠z = 132°

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Additional comment

The relations we used are ...

• vertical angles are congruent
• sum of angles in a triangle is 180°
• an exterior angle is equal to the sum of the remote interior angles