Question

the two triangles below are similar. also, m∠z=20° and m∠x=100° as shown below. find m∠g, m∠h, and m∠i. assume the triangles are accurately drawn.

Explanation:

Step1: Recall properties of similar triangles

Similar triangles have corresponding angles equal. Also, the sum of angles in a triangle is \(180^\circ\). First, find the third angle of triangle \(XYZ\). Let \(\angle Y\) be the third angle. So, \(m\angle Y=180^\circ - m\angle Z - m\angle X\). Substituting values: \(m\angle Y = 180^\circ - 20^\circ - 100^\circ=60^\circ\).

Step2: Identify corresponding angles

From the diagram (assuming correspondence: \(\angle X\) corresponds to \(\angle G\), \(\angle Z\) corresponds to \(\angle H\), \(\angle Y\) corresponds to \(\angle I\)) because of similar triangles. So:

• \(m\angle G = m\angle X = 100^\circ\) (corresponding angles of similar triangles)
• \(m\angle H = m\angle Z = 20^\circ\) (corresponding angles of similar triangles)
• \(m\angle I = m\angle Y = 60^\circ\) (corresponding angles of similar triangles)

Answer:

\(m\angle G = \boldsymbol{100}^\circ\), \(m\angle H = \boldsymbol{20}^\circ\), \(m\angle I = \boldsymbol{60}^\circ\)