Triangle xyz is isosceles. Angle y measures $a$ degrees. What expression represents the measure of angle x?

• A. $\frac{180-a}{2}$
• B. $90-a$
• C. $180-a$
• D. $a$

Answer: (A)

Verified step by step guidance

1. Recall that in any triangle, the sum of the interior angles is always \$180^\circ\(. So, we have the equation: \)x + y + z = 180$.
2. Since triangle XYZ is isosceles, two of its angles are equal. Identify which angles are equal. Given that angle \(y\) measures \(a\) degrees, the other two angles, \(x\) and \(z\), must be equal.
3. Set \(x = z\) because the triangle is isosceles and these two angles are the ones opposite the equal sides.
4. Substitute \(z\) with \(x\) and \(y\) with \(a\) in the angle sum equation: \(x + a + x = 180\).
5. Combine like terms to get \$2x + a = 180\(, then solve for \)x\( by isolating it: \)x = \frac{180 - a}{2}$.