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: Recall isosceles triangle properties

In an isosceles triangle, the angles opposite the equal sides are equal. From the diagram, sides \(XY\) and \(XZ\) are equal (marked with ticks), so angles opposite them (angle \(Z\) and angle \(Y\)) are equal. Thus, \(\angle Z=\angle Y = a^{\circ}\).

Step2: Use triangle angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(\angle X = x\). Then \(x + \angle Y+\angle Z=180^{\circ}\). Substituting \(\angle Y = a^{\circ}\) and \(\angle Z = a^{\circ}\), we get \(x + a + a=180\).

Step3: Solve for \(x\)

Simplify the equation: \(x + 2a=180\). Subtract \(2a\) from both sides: \(x = 180 - 2a\). So the measure of angle \(X\) is \(180 - 2a\) degrees.

Answer:

\(180 - 2a\) (corresponding to the option "180 - 2a")