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?

Given:

In ΔEFG and ΔYXZ, ∠F ≅ ∠X and ∠E ≅ ∠Y. If m∠E = 62° and m∠X = 80°.

To find:

The measure of ∠Z.

Solution:

In ΔEFG and ΔYXZ,

∠F ≅ ∠X

m∠F = m∠X = 80°

∠E ≅ ∠Y

m∠E = m∠Y = 62°

Now, in ΔYXZ,

     [Angle sum property]

Therefore, the measure of ∠Z is 38°.

step-by-step explanation: