Question

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?


triangles EFG and YXZ in which triangle YXZ is larger than EFG


38°

62°

80°

142°

Answer 1

Answer:

$m\angle F = 80^o$

Step-by-step explanation:

we know that

The AA Similarity Theorem states: If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

In this problem

Triangles EFG and YXZ are similar by AA Similarity Theorem

Because

m∠F ≅ m∠X  and m∠E ≅ m∠Y

Remember that in a triangle the sum of the interior angles must be equal to 180 degrees

so

m∠G ≅ m∠Z

we have

m∠E = 62°

m∠X = 80°

Remember that

m∠F ≅ m∠X

therefore

$m\angle F = 80^o$

Answer 2

Answer:

38

Step-by-step explanation:

Congruent angles of different proportions does not effect the measurement of interior angles...they equal 180.  62+80+28=180