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? Check all that apply.
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 creates two smaller isosceles triangles.

Answer 1

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

To find :  What is true about triangle XYZ

Solution:

Let say Base angle  = A

=> ∠X = ∠Z =  A

The measure of the vertex angle, Y, is twice the measure of a base angle

=> ∠Y = 2A

∠X +  ∠Y  +  ∠Z  = 180°

=> A + 2A  + A = 180°

=>  4A = 180°

=>   A = 45°

=>  ∠X = ∠Z =   45°   & ∠Y = 90°

Angle Y is a right angle.  - TRUE

The measure of angle Z is 45° - TRUE

The measure of angle X is 36°. - FALSE

The measure of the vertex angle is 72°. - FALSE

The perpendicular bisector of Base creates two smaller isosceles triangles. - TRUE

as its isosceles triangle  ( perpendicular bisector of base will be angle bisector of Y also)

=>  ∠Y/2 = 90°/2 = 45°

∠X = ∠Z =   45°  

Hence  two smaller isosceles triangles. created

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