Question

triangle xyz is isosceles. angle y measures a°. what expression represents the measure of angle x? 2a \\( \frac { a } { 2 } \\) 90 - a 180 - 2a

Explanation:

Step1: Use the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(\angle X+\angle Y+\angle Z = 180^{\circ}\).

Step2: Use the property of isosceles triangle

Since \(\triangle XYZ\) is isosceles and \(XY = XZ\) (marked in the figure), then \(\angle Y=\angle Z=a^{\circ}\).
Substitute \(\angle Y = a^{\circ}\) and \(\angle Z=a^{\circ}\) into \(\angle X+\angle Y+\angle Z = 180^{\circ}\). We get \(\angle X+a + a=180\).

Step3: Solve for \(\angle X\)

\(\angle X=180-(a + a)=180 - 2a\)

Answer:

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