Question

what is the value of z? z = °

Explanation:

Step1: Identify triangle type

The markings on the sides indicate that $\triangle GFH$ is isosceles with $GF = FH$. In an isosceles triangle, base - angles are equal.

Step2: Recall angle - sum property of a triangle

The sum of interior angles of a triangle is $180^{\circ}$. Let $\angle F = 36^{\circ}$, and since base - angles are equal, if $\angle G=z$ and $\angle H$ are the base - angles, we have $z + z+36^{\circ}=180^{\circ}$.

Step3: Solve the equation for $z$

Combining like terms gives $2z=180^{\circ}- 36^{\circ}=144^{\circ}$. Then $z=\frac{144^{\circ}}{2}=72^{\circ}$.

Answer:

$72$