In triangle XYZ, A is a point on YZ such that XA=YA. IF ∠ XYA = 50° and ∠ AXZ = 19° what is the degree measures of ∠XZA?

In triangle XYZ, A is a point on YZ such that XA=YA. IF ∠…

In triangle XYZ, A is a point on YZ such that XA=YA. IF $\angle$ XYA = 50° and $\angle$ AXZ = 19° what is the degree measures of ∠XZA?

Show answer & explanation

Correct answer: A

Explanation

The correct answer is option 1 i.e. 61°.

∠XYA = 50° and ∠AXZ = 19°

XA = YA

So, triangle XYA is isosceles. Thus, ∠XYA = ∠YXA = 50°

The sum of angles in a triangle is 180°.

∠YAX = 180° - (∠XYA + ∠YXA) = 180° - (50° + 50°) = 180° - 100° = 80°

∠XAZ = 180° - ∠YAX = 180° - 80° = 100°.

Then, ∠XZA = 180° - (∠AXZ + ∠XAZ) = 180° - (19° + 100°) = 180° - 119° = 61°

Therefore, the measure of ∠XZA is 61°.