7
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Question 7 • Mathematics II

Triangle XYZ is isoceles. The measure of the vertex angle, cap y , is twice the measure of a base angle. What is true about triangle XYZ ? Choose three correct answers.

Answer
A
The measure of angle cap z is 45 degrees .
B
The measure of angle cap x is 36 degrees .
C
The perpendicular bisector of line segment XZ creates two smaller isosceles triangles.
D
The measure of the vertex angle is 72 degrees .
E
Angle cap y is a right angle.

Explanation

The two base angles are equal. If each is x, then the vertex angle is 2x, so x + x + 2x = 180°; therefore x = 45° and angle y = 90°. This makes B true and angle z = 45°, so E is true. The perpendicular bisector of XZ passes through Y and divides the triangle into two 45°-45°-90° triangles, which are isosceles, so A is true.

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