Question

isosceles triangle $\triangle xyz$ is shown, along with some of its measures. determine $x$, the measure of $angle x$. $x=$ degrees

Explanation:

Step1: Use the property of isosceles triangle

In an isosceles triangle \( \triangle XYZ\), \(XY = YZ\), so \( \angle X=\angle Z=x^{\circ}\).

Step2: Apply the triangle - angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So \(x + x+50=180\).
Simplify the left - hand side: \(2x+50 = 180\).
Subtract 50 from both sides: \(2x=180 - 50\), \(2x = 130\).
Divide both sides by 2: \(x=\frac{130}{2}\).

Answer:

\(65\)