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

Answer 1

Answer:

angle y is a right angle

the measure of angle Z is 45 degrees

the perpendicular bisector of line XZ creates two smaller isosceles triangles

Step-by-step explanation:

Answer 2

Answer:

a. Angle Y is a right angle.

b. The measure of angle Z is 45°.

e. The perpendicular bisector of creates two smaller isosceles triangles.

Step-by-step explanation:

Let x represent the measures of base angles X and Z. Then 2x is the measure of vertex angle Y, and the sum of angles is ...

  x + x + 2x = 180°

  x = 45°

  2x = m∠Y = 90°

so the triangle is an isosceles right triangle which has base angles of 45°.

The perpendicular bisector of XZ is the altitude of the triangle XYZ. It creates two smaller right triangles with acute angles of 45°. Hence, those, too, are isosceles right triangles.