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.
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.
2 answers:
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.
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