Question

in △ghi, $overline{gh}congoverline{ig}$ and $mangle i = 36^{circ}$. find $mangle g$.

Explanation:

Step1: Identify the isosceles - triangle

Since $\overline{GH}\cong\overline{IG}$ in $\triangle GHI$, $\triangle GHI$ is an isosceles triangle with base - angles $\angle H$ and $\angle I$.

Step2: Recall the property of isosceles triangle

In an isosceles triangle, base - angles are equal. So, $m\angle H=m\angle I = 36^{\circ}$.

Step3: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. So, $m\angle G+m\angle H+m\angle I=180^{\circ}$.

Step4: Solve for $m\angle G$

Substitute $m\angle H = 36^{\circ}$ and $m\angle I = 36^{\circ}$ into the equation: $m\angle G+36^{\circ}+36^{\circ}=180^{\circ}$. Then $m\angle G=180^{\circ}-(36^{\circ}+36^{\circ})=108^{\circ}$.

Answer:

$108^{\circ}$