Question

1. find the value of x.
2. find ( mangle wyz ).

Explanation:

Step1: Use the property of isosceles triangle

In an isosceles triangle, the base - angles are equal. Here, the two angles \((6x + 1)^{\circ}\) and \((9x-23)^{\circ}\) are equal. So, we set up the equation \(6x + 1=9x-23\).

Step2: Solve the equation for \(x\)

Subtract \(6x\) from both sides:
\(6x + 1-6x=9x-23 - 6x\)
\(1 = 3x-23\)
Add \(23\) to both sides:
\(1+23=3x-23 + 23\)
\(24 = 3x\)
Divide both sides by \(3\):
\(x=\frac{24}{3}\)
\(x = 8\)

Answer:

\(x = 8\)