Answer:
∠C = 70°
Step-by-step explanation:
When dealing with similar triangles, the angles of both triangles are equal. With that being said, the letters of those angles typically corralete as well. In this case, we have ΔABC and ΔDEF. Based on the way those letters are arranged, we can assume the following:
∠A = ∠D
∠B = ∠E
∠C = ∠F
The question tells us ∠A = 36°. Since we know that ∠A is equal to ∠D, we know that ∠D also equals 36°. The question also tells us ∠E = 74°. Once again, since we know that ∠E is equal to ∠B, we know that ∠B is 74° as well.
Now we use that information to solve for ∠C. The sum of the angles of a triangle always adds up to 180°. Because we know that, we can solve easily:
180 - (36 + 74) = 70
∴ ∠C = 70°
