Question

question
in △hij, $overline{hi}congoverline{jh}$ and m∠j = 34°. find m∠i.
answer attempt 1 out of 2

Explanation:

Step1: Identify isosceles - triangle

Since $\overline{HI}\cong\overline{JH}$ in $\triangle HIJ$, $\triangle HIJ$ is an isosceles triangle. The base - angles are equal. So $\angle J=\angle H = 34^{\circ}$.

Step2: Use angle - sum property of triangle

The sum of the interior angles of a triangle is $180^{\circ}$. Let $m\angle I=x$. Then $m\angle H + m\angle J+m\angle I=180^{\circ}$. Substitute $m\angle H = 34^{\circ}$ and $m\angle J = 34^{\circ}$ into the equation: $34^{\circ}+34^{\circ}+x = 180^{\circ}$.

Step3: Solve for $x$

First, simplify the left - hand side: $68^{\circ}+x = 180^{\circ}$. Then subtract $68^{\circ}$ from both sides: $x=180^{\circ}-68^{\circ}=112^{\circ}$.

Answer:

$112^{\circ}$