Question

question in △ghi, (overline{ig}congoverline{hi}) and (mangle h = 51^{circ}). find (mangle g).

Explanation:

Step1: Identify the triangle type

Since $\overline{IG}\cong\overline{HI}$, $\triangle GHI$ is isosceles. In an isosceles triangle, base - angles are equal. Let $\angle G=\angle I = x$.

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. So, $m\angle G + m\angle H+m\angle I=180^{\circ}$. Substitute $m\angle H = 51^{\circ}$ and $m\angle G=m\angle I = x$ into the equation: $x + 51^{\circ}+x=180^{\circ}$.

Step3: Solve the equation for $x$

Combine like - terms: $2x+51^{\circ}=180^{\circ}$. Subtract $51^{\circ}$ from both sides: $2x=180^{\circ}- 51^{\circ}=129^{\circ}$. Then divide both sides by 2: $x=\frac{129^{\circ}}{2}=64.5^{\circ}$.

Answer:

$64.5^{\circ}$