Question

question 4 (multiple choice worth 1 points) (03.05pr mc) in δefg and δyxz, m∠f ≅ m∠x and m∠e ≅ m∠y. if m∠e = 62° and m∠x = 80°, what is the measure of ∠z? image of two triangles: δefg with vertices e, f, g and δyxz with vertices y, x, z options: 38°, 62°, 80°, 142°

Explanation:

Step1: Identify congruent angles

Given \( m\angle E \cong m\angle Y \) and \( m\angle E = 62^\circ \), so \( m\angle Y = 62^\circ \). Also, \( m\angle F \cong m\angle X \) and \( m\angle X = 80^\circ \), so \( m\angle F = 80^\circ \). But we need \( \angle Z \) in \( \triangle YXZ \). The sum of angles in a triangle is \( 180^\circ \).

Step2: Calculate \( m\angle Z \)

In \( \triangle YXZ \), \( m\angle Y + m\angle X + m\angle Z = 180^\circ \). Substitute \( m\angle Y = 62^\circ \) and \( m\angle X = 80^\circ \):
\( 62^\circ + 80^\circ + m\angle Z = 180^\circ \)
\( 142^\circ + m\angle Z = 180^\circ \)
\( m\angle Z = 180^\circ - 142^\circ = 38^\circ \)

Answer:

\( 38^\circ \)