MATH SOLVE

3 months ago

Q:
# 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.

Accepted Solution

A:

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.