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 ∠Z?

Answer 1

∠Z=38°.

Explanation:

Given: ∠E ≅ ∠Y, ∠F ≅ ∠X ≅ ∠∠X and ∠X = 80°.

Refer to the image below:

Since ∠E ≅ ∠Y and ∠F ≅ ∠X, this muse mean that ∠G ≅ ∠Z. Now if ∠X = 80°, ∠F has to equal the same since the two are congruent. If you substitute the rest based off of the given, ∠Z=38°.

Answer 2

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,

`m\angle X+m\angle Y+m\angle Z=180^\circ` [Angle sum property]

`80^\circ+62^\circ+m\angle Z=180^\circ`

`142^\circ+m\angle Z=180^\circ`

`m\angle Z=180^\circ-142^\circ`

`m\angle Z=38^\circ`

Therefore, the measure of ∠Z is 38°.