Question

find ( mangle ihg ).

Explanation:

Step1: Identify the triangle type

Since \(IH = HG\), \(\triangle IHG\) is an isosceles triangle. In an isosceles triangle, the angles opposite the equal sides are equal. So, \(\angle I=\angle G = 30^{\circ}\).

Step2: Use the triangle - angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(m\angle IHG=x\). Then, using the formula \(\angle I+\angle G+\angle IHG = 180^{\circ}\). Substitute \(\angle I = 30^{\circ}\) and \(\angle G=30^{\circ}\) into the formula: \(30^{\circ}+30^{\circ}+x = 180^{\circ}\).

Step3: Solve for \(x\)

Simplify the left - hand side of the equation: \(60^{\circ}+x = 180^{\circ}\). Subtract \(60^{\circ}\) from both sides: \(x=180^{\circ}-60^{\circ}=120^{\circ}\).

Answer:

\(120^{\circ}\)