Question

In Δfgh ≅ Δlmn, m∠f = 52°, and m∠m = 67°. In blank 1, give the measure of ∠h. Give your answer as just a number; no degrees. In blank 2, give the theorem that helped you solve this problem.

Answer 1

The measure of ∠h in Δfgh is 61°. To find this, we apply the Triangle Sum Theorem, stating that the sum of the interior angles of a triangle is always 180°, and subtract the known angle measurements from 180°.

Step-by-step explanation:

To find the measure of ∠h in Δfgh, which is congruent to Δlmn, we can use the fact that corresponding angles in congruent triangles are equal. We are given that m∠f = 52° and m∠m = 67°. Since m∠m corresponds to m∠h, m∠h also equals 67°. Additionally, the sum of the angles in any triangle is 180°, so we can find the measure of ∠h by subtracting the known angles from 180°:

180° - m∠f - m∠m = 180° - 52° - 67° = 61°.

∠h is 61°. The Theorem that helps us solve this problem is the Triangle Sum Theorem, which states that the sum of the interior angles of a triangle is always 180°.