Question

In triangles Δefg and Δyxz, if m∠f ≅ m∠x and m∠e ≅ m∠y, and given that m∠e = 62° and m∠x = 80°, what is the measure of ∠f?

1) 38°
2) 62°
3) 80°
4) 142°

Answer 1

The measure of ∠f in triangle Δefg, given that m∠f ≅ m∠x and m∠e = 62° and m∠x = 80°, is 38°.

Step-by-step explanation:

The question asks for the measure of ∠f in triangles Δefg and Δyxz, given that m∠f ≅ m∠x and m∠e ≅ m∠y, with m∠e = 62° and m∠x = 80°. To solve for the measure of ∠f, we can use the fact that the sum of angles in a triangle is always 180°. Since we know two of the three angles in triangle Δefg (m∠e and m∠f), we can find the third angle by subtracting the sum of the known angles from 180°.

m∠e + m∠f + m∠g = 180° (Sum of angles in a triangle).

Given m∠e = 62° and m∠f = m∠x = 80°, we have:

62° + 80° + m∠g = 180°

142° + m∠g = 180°

m∠g = 180° - 142°

m∠g = 38°

Therefore, the measure of ∠f is 38°, which corresponds to option 1).