Question

what is the value of z?

Explanation:

Step1: Identify the triangle type

Since two sides of the triangle are equal (marked with the same tick marks), it is an isosceles triangle. In an isosceles triangle, the base - angles are equal. Let the measure of each base - angle be \(z\).

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(z + z+40^{\circ}=180^{\circ}\).
Simplify the left - hand side: \(2z+40^{\circ}=180^{\circ}\).
Subtract \(40^{\circ}\) from both sides: \(2z=180^{\circ}- 40^{\circ}\), so \(2z = 140^{\circ}\).
Divide both sides by 2: \(z=\frac{140^{\circ}}{2}\).

Answer:

\(70\)