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------------------------------------------------ What is the measure of Angle Y in triangle XYZ?

Given:
- Angle X is 65 degrees
- Angle Z is 53 degrees
- Angle Y is unknown

A) 62 degrees
B) 72 degrees
C) 80 degrees
D) 100 degrees

By using the Triangle Angle Sum theorem, which states that the sum of the angles of a triangle equals 180 degrees, we subtract the known angles (X and Z) from 180. Thus we find that the measure of Angle Y in the triangle XYZ is 62 degrees.

Explanation:

In a triangle, the sum of all the angles is equal to 180 degrees. This is known as the Triangle Angle Sum theorem. Given that the triangle XYZ has angle X with 65 degrees and angle Z with 53 degrees, we can use this theorem to find the value of angle Y. We subtract the measure of angles X and Z from 180 degrees.

So, the calculation will be: Angle Y = 180 - (Angle X + Angle Z) = 180 - (65 + 53) = 62 degrees.

Therefore, the measure of angle Y in triangle XYZ is 62 degrees which corresponds to option A.

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