Question

In triangles EFG and YXZ, m∠F ≅ m∠X, and m∠E ≅ m∠Y. If m∠E = 62° and m∠X = 80°, what is the measure of ∠F? Triangles EFG and YXZ, in which triangle YXZ is larger than EFG.

Select one:
a. 38°
b. 62°
c. 80°
d. 142°

Answer 1

The measure of ∠F in the triangle is 80° because it is congruent to ∠X, which is also 80°.

Step-by-step explanation:

The question asks us to find the measure of ∠F in a pair of triangles with two pairs of congruent angles. Since the triangles EFG and YXZ have two pairs of angles that are congruent (∠F ≅ ∠X and ∠E ≅ ∠Y) and we know that the sum of angles in any triangle is always 180°, we can use this information to find the measure of ∠F.

We are given that:

• m∠E = 62°
• m∠X = 80°

Since ∠F and ∠X are congruent:

• m∠F = m∠X = 80°

Therefore, the measure of ∠F is 80°.