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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,
[tex]m\angle X+m\angle Y+m\angle Z=180^\circ[/tex] [Angle sum property]
[tex]80^\circ+62^\circ+m\angle Z=180^\circ[/tex]
[tex]142^\circ+m\angle Z=180^\circ[/tex]
[tex]m\angle Z=180^\circ-142^\circ[/tex]
[tex]m\angle Z=38^\circ[/tex]
Therefore, the measure of ∠Z is 38°.
Answer:
∠Z=38°.
Step-by-step 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°.
