Question

triangle xyz is isosceles. angle y measures a°. what expression represents the measure of angle x? 2a a/2 90 - a 180 - 2a

Explanation:

Step1: Recall the properties of an isosceles triangle

In an isosceles triangle \( \triangle XYZ\), \( \angle Y=\angle Z = a^{\circ}\) (since sides opposite equal angles are equal and vice - versa).

Step2: Use the angle - sum property of a triangle

The sum of angles in a triangle is \(180^{\circ}\). Let \( \angle X=x\). Then \(x + \angle Y+\angle Z=180^{\circ}\).
Substitute \( \angle Y = a^{\circ}\) and \( \angle Z = a^{\circ}\) into the equation: \(x+a + a=180^{\circ}\).

Step3: Solve for \(x\)

Combine like terms: \(x + 2a=180^{\circ}\).
Subtract \(2a\) from both sides: \(x=180 - 2a\).

Answer:

\(180 - 2a\) (the option \(180 - 2a\))