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 ∠F?

38° 62° 80° 142°

In triangles \( \triangle EFG \) and \( \triangle YXZ \), we know the following:

1. \( m\angle F \cong m\angle X \)
2. \( m\angle E \cong m\angle Y \)
3. \( m\angle E = 62^\circ \) and \( m\angle X = 80^\circ \)

Since the sum of angles in a triangle is always \(180^\circ\), we can find the measure of \( m\angle F \) as follows:

Given:
\[
m\angle E + m\angle F + m\angle G = 180^\circ
\]
Substituting \( m\angle E = 62^\circ \) and \( m\angle F = 80^\circ \):
\[
62^\circ + 80^\circ + m\angle G = 180^\circ
\]

Solving for \( m\angle G \):
\[
m\angle G = 180^\circ - 142^\circ = 38^\circ
\]

Thus, the measure of \( m\angle F \) is **80°**.

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Do you need further clarification on any of these steps, or have additional questions?

1. What is the Triangle Sum Theorem?
2. How can angle congruence help in solving triangle problems?
3. What if only two angles were given in each triangle?
4. Can two triangles be similar with only angle information?
5. How do congruent angles affect triangle congruence?

**Tip:** In any triangle, knowing two angles allows you to find the third by subtracting their sum from 180°.

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 ∠F? Options: 38°, 62°, 80°, 142°

Solve for the missing angle in ΔEFG with m∠E = 62° and m∠X = 80° using triangle sum theorem and congruent angles. Suitable for Grades 8-10, this problem helps students understand key geometric principles like angle sums in triangles and congruence.

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