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:

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.

Answer 2

From the resulting angles, we can deduce the following;

• Angle Y is a right angle.
• The measure of angle Z is 45°
• The perpendicular bisector creates two smaller isosceles triangles:

Options A, B and C are correct

For an isosceles triangle, the base angles are equal.

For the triangle XYZ, the sum of the interior angle is 180degrees, hence;

m<X + m<Y + m<Z = 180

Since the base angles m<X = m<Z

The expression becomes

m<X + m<Y + m<X = 190

2m<X + m<Y = 180

If the measure of the vertex angle, Y, is twice the measure of a base angle, then m<Y = 2m<X

The resulting expression becomes:

2m<X + m<Y = 180

2m<X + 2m<X= 180

4m<X = 180

m<X = 180/4

m<X = 45 degrees

Since m<X = m<Z, m<Z =45 degrees

m<Y = 180 - (45 + 45)

m<Y = 180 - 90

m<Y = 90degrees

From the resulting angles, we can deduce the following;

• Angle Y is a right angle.
• The measure of angle Z is 45°

Learn more here: https://brainly.com/question/2911081