Question

what is the value of z?

Explanation:

Step1: Use the property of isosceles triangle

Since two sides of the triangle are equal (marked with the same tick), the triangle is isosceles. In an isosceles triangle, the base - angles are equal. Let the two equal angles be \(z\) and the third angle is \(52^{\circ}\).

Step2: Apply the angle - sum property of a triangle

The sum of angles in a triangle is \(180^{\circ}\). So, \(z + z+52^{\circ}=180^{\circ}\), which simplifies to \(2z=180^{\circ}- 52^{\circ}\).

$$2z = 128^{\circ}$$

Step3: Solve for \(z\)

Divide both sides of the equation \(2z = 128^{\circ}\) by \(2\).

$$z=\frac{128^{\circ}}{2}=64^{\circ}$$

Answer:

\(64\)