Question

In △FGH ≅ △LMN, m∠F=52°, and m∠M=67°, what is the measure of ∠H?

a. 61
b. 119
c. 113
d. 67

Answer 1

The measure of ∠H in △FGH, which is congruent to △LMN, is 61°, determined by subtracting the measure of the other two angles from 180°.

Step-by-step explanation:

To find the measure of ∠H in △FGH ≅ △LMN, first, we need to understand that congruent triangles have corresponding angles with equal measures. Knowing that the sum of the angles in any triangle is always 180°, we can use the given measures of ∠F and ∠M to find the measure of ∠H.

Since ∠F = 52°, and by the property of congruent triangles, the angle corresponding to ∠F in △LMN is also 52°, which would be ∠L. Now, we know that ∠M is 67°. Using these values, we can find the third angle in △LMN, which would be ∠N, by calculating 180° - 52° - 67° = 61°. This angle corresponds to ∠H in △FGH. Therefore, the measure of ∠H is 61°.