Question

the two triangles below are similar. also, m∠h = 20° and m∠g = 95° as shown below. find m∠x, m∠y, and m∠z. assume the triangles are accurately drawn. two triangles are shown: one with vertices g, h, i (∠g=95°, ∠h=20°) and another with vertices z, y, x m∠x = □° m∠y = □° m∠z = □°

Explanation:

Step1: Find angle at I in triangle GHI

In triangle \( GHI \), the sum of angles in a triangle is \( 180^\circ \). So, \( m\angle I = 180^\circ - m\angle G - m\angle H \). Substituting \( m\angle G = 95^\circ \) and \( m\angle H = 20^\circ \), we get \( m\angle I = 180 - 95 - 20 = 65^\circ \).

Step2: Use similarity to find angles in triangle XYZ

Since the triangles are similar, corresponding angles are equal.

• \( \angle X \) corresponds to \( \angle G \), so \( m\angle X = 95^\circ \).
• \( \angle Y \) corresponds to \( \angle I \), so \( m\angle Y = 65^\circ \).
• \( \angle Z \) corresponds to \( \angle H \), so \( m\angle Z = 20^\circ \).

Answer:

\( m\angle X = 95^\circ \), \( m\angle Y = 65^\circ \), \( m\angle Z = 20^\circ \)