triangle xyz is isosceles. angle y measures a°. what expression represents the measure of angle x? 2a…

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

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

Answer

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In (\triangle XYZ), let (\angle X=x), (\angle Y = a^{\circ}), and (\angle Z). Since (\triangle XYZ) is isosceles and the base - angles of an isosceles triangle are equal, if (\angle Y) is one of the base - angles, then (\angle Z=\angle Y = a^{\circ}).

Step2: Set up the angle - sum equation

We know that (x + a+a=180).

Step3: Solve for (x)

Combining like terms, we get (x+2a = 180). Then, subtracting (2a) from both sides of the equation, we have (x=180 - 2a).

Answer:

(180 - 2a)