Question

Triangle XYZ is isosceles. The measure of the vertex angle, Y, is twice the measure of a base angle.

What is true about triangle XYZ? Select three options.

Angle Y is a right angle.
The measure of angle Z is 45°.
The measure of angle X is 36°.
The measure of the vertex angle is 72°.
The perpendicular bisector of Line segment X Z creates two smaller isosceles triangles.

Answer 1

The answer is A, the measure of angle Z is 45°.

Step-by-step explanation: According to base angle theorem for iscoscles triangles, the base angles must be the same angle measure if the sides opposite to them are congruent. Since it is an iscoceles triangle, they are automatically congruent. This means that Y is 90 degrees. This fits into triangle sum theorem because if Z is 45 degrees, than x is also 45 degrees making a viable triangle. This means that this is the only one that actually applies. B is wrong because of triangle sum theorem, C is wrong because of triangle sum theorem, and D is wrong because of the SSS postulate and CPCTC.

Answer 2

A. Angle Y is a right angle.

B. The measure of angle Z is 45°.

E. The perpendicular bisector of Line segment X Z creates two smaller isosceles triangles.

Explanation:

I hope these are correct and help you guys.