Question

Triangle XYZ is isosceles. Angle Y measures a°.

Triangle X Y Z is shown. The lengths of sides Y X and Z X are congruent. Angle X Y Z is a degrees.

What expression represents the measure of angle X?
A. 2a
B. a/2
C. 90-a
D. 80-2a

Answer 1

In an isosceles triangle XYZ with angle Y measured as 'a' degrees, the measure of angle X is '180 - 2a' degrees. The correct answer, given a typographical error in the options, would be '180 - 2a', closest to option D, '80 - 2a'.

Step-by-step explanation:

The question deals with finding the measure of angle X in an isosceles triangle XYZ with given angles. To solve this, we can use the fact that the sum of all angles in a triangle equals 180 degrees. In an isosceles triangle, the angles at the base are equal, so if angle Y is a degrees, then angle Z is also a degrees. Angle X, being the vertex angle, will then be:

Angle X = 180 degrees - (Angle Y + Angle Z)

Angle X = 180 degrees - (a + a)

Angle X = 180 degrees - 2a

Therefore, the correct expression representing the measure of angle X is 180 - 2a. However, given the provided options the closest one is D. 80 - 2a, assuming there is a typo and it should have been written as 180 - 2a.