Question

question
find m∠ihg.
answer attempt 1 out of 2
m∠ihg=° submit answer

Explanation:

Step1: Determine the type of triangle

Since two sides of the triangle \( \triangle IHG \) are marked as equal (the sides opposite \( \angle I \) and \( \angle G \)), \( \triangle IHG \) is an isosceles triangle. In an isosceles triangle, the angles opposite the equal sides are equal. So \( \angle I=\angle G = 50^{\circ}\).

Step2: Use the triangle - angle sum property

The sum of the interior angles of a triangle is \( 180^{\circ}\). Let \( \angle IHG=x\). Then, using the formula \( \angle I+\angle G+\angle IHG = 180^{\circ}\).
Substitute \( \angle I = 50^{\circ}\) and \( \angle G=50^{\circ}\) into the formula: \(50^{\circ}+50^{\circ}+x = 180^{\circ}\).
Simplify the left - hand side: \(100^{\circ}+x = 180^{\circ}\).
Solve for \(x\): \(x=180^{\circ}-100^{\circ}\).

Answer:

\(80\)