Question

in $\triangle ghi, \overline{gh} \cong \overline{ig}$ and $m\angle i = 69^\circ$. find $m\angle h$.

Explanation:

Step1: Identify triangle type

$\triangle GHI$ is isosceles with $\overline{GH} \cong \overline{IG}$, so base angles $\angle H$ and $\angle G$ are congruent.

Step2: Recall triangle angle sum

The sum of angles in a triangle is $180^\circ$. Let $\text{m}\angle H = \text{m}\angle G = x$.

Step3: Set up angle sum equation

$$x + x + 69^\circ = 180^\circ$$

Step4: Solve for $x$

$$2x = 180^\circ - 69^\circ$$
$$2x = 111^\circ$$
$$x = \frac{111^\circ}{2} = 55.5^\circ$$

Answer:

$\text{m}\angle H = 55.5^\circ$