Question

question
in △hij, $overline{jh}congoverline{ij}$ and m∠i = 76°. find m∠j.

Explanation:

Step1: Identify the triangle type

Since $\overline{JH}\cong\overline{IJ}$, $\triangle HIJ$ is isosceles. In an isosceles triangle, base - angles are equal.

Step2: Use angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. Let $m\angle J = m\angle H=x$. Then $x + x+76^{\circ}=180^{\circ}$.

Step3: Solve the equation for $x$

Combining like - terms gives $2x+76^{\circ}=180^{\circ}$. Subtract $76^{\circ}$ from both sides: $2x=180^{\circ}-76^{\circ}=104^{\circ}$. Divide both sides by 2: $x = 52^{\circ}$. So $m\angle J = 52^{\circ}$.

Answer:

$52^{\circ}$