Question

the two triangles below are similar. also, m ∠ z = 20° and m ∠ y = 110° as shown below. find m ∠ g, m ∠ h, and m ∠ i. assume the triangles are accurately drawn.

Explanation:

Step1: Find angle X in triangle XYZ

The sum of angles in a triangle is \(180^\circ\). So, \(m\angle X = 180^\circ - m\angle Y - m\angle Z\). Substituting the given values: \(m\angle X = 180^\circ - 110^\circ - 20^\circ = 50^\circ\).

Step2: Use similarity of triangles

Since triangles XYZ and IHG are similar, corresponding angles are equal. So, \(m\angle G = m\angle Y = 110^\circ\) (corresponding angles), \(m\angle H = m\angle X = 50^\circ\) (corresponding angles), and \(m\angle I = m\angle Z = 20^\circ\) (corresponding angles).

Answer:

\(m\angle G = 110^\circ\), \(m\angle H = 50^\circ\), \(m\angle I = 20^\circ\)