Questions: In triangle GHI, GH is congruent to IG and m angle I=36 degrees. Find m angle G.

Solution Steps

To solve for $\mathrm{m} \angle G$ in $\triangle GHI$ where $\overline{GH} \cong \overline{IG}$ and $\mathrm{m} \angle I = 36^{\circ}$, we can use the properties of isosceles triangles. Since $\overline{GH} \cong \overline{IG}$, $\triangle GHI$ is isosceles with $\angle G = \angle H$. The sum of the angles in any triangle is $180^\circ$. Therefore, we can set up an equation to solve for $\angle G$.

1. Recognize that $\triangle GHI$ is isosceles with $\angle G = \angle H$.
2. Use the fact that the sum of the angles in a triangle is $180^\circ$.
3. Set up the equation: $\angle G + \angle H + \angle I = 180^\circ$.
4. Since $\angle G = \angle H$, substitute $\angle G$ for $\angle H$ in the equation.
5. Solve for $\angle G$.

In triangle \( GHI \), we know that \( \overline{GH} \cong \overline{IG} \), which implies that \( \angle G = \angle H \). We are also given that \( \mathrm{m} \angle I = 36^\circ \).

Using the property that the sum of the angles in a triangle is \( 180^\circ \), we can write the equation: \[ \angle G + \angle H + \angle I = 180^\circ \] Since \( \angle G = \angle H \), we can substitute: \[ 2 \cdot \angle G + 36^\circ = 180^\circ \]

Rearranging the equation gives: \[ 2 \cdot \angle G = 180^\circ - 36^\circ \] \[ 2 \cdot \angle G = 144^\circ \] Dividing both sides by 2, we find: \[ \angle G = \frac{144^\circ}{2} = 72^\circ \]

Final Answer