Question

triangle xyz is isosceles. angle y measures a° (diagram of triangle xyz with y and z at base, x at top, angle y is a°). what expression represents the measure of angle x? options: 2a, \\(\frac{a}{2}\\), 90 - a, 180 - 2a

Explanation:

Step1: Identify isosceles triangle properties

In isosceles triangle \( XYZ \), sides \( XY = XZ \) (from the diagram, equal sides imply equal base angles), so \( \angle Y=\angle Z = a^\circ \).

Step2: Use triangle angle sum theorem

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

Step3: Solve for \( x \)

Simplify the equation: \( x + 2a=180^\circ \), so \( x = 180 - 2a \).

Answer:

\( 180 - 2a \) (corresponding option: the one with \( 180 - 2a \))