Question

question
in △ghi, $overline{gh}congoverline{ig}$ and m∠i = 51°. find m∠g.

Explanation:

Step1: Identify isosceles - triangle property

Since $\overline{GH}\cong\overline{IG}$ in $\triangle GHI$, $\angle H=\angle I$.

Step2: Recall angle - sum property of a triangle

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

Step3: Substitute the known values

We know $m\angle I = 51^{\circ}$ and $m\angle H = 51^{\circ}$. Then $m\angle G+51^{\circ}+51^{\circ}=180^{\circ}$.

Step4: Solve for $m\angle G$

$m\angle G=180^{\circ}-(51^{\circ}+51^{\circ})=180^{\circ}-102^{\circ}=78^{\circ}$.

Answer:

$78^{\circ}$