Question

In triangle ALMN, where MN - LM and m/M = 45°, find m/L.

A) 45°
B) 90°
C) 135°
D) 180°

Answer 1

In triangle ALMN with sides MN = LM and m/M = 45°, m/L is also 45° since it is an isosceles triangle. This makes m/L equal to 45° (Option A).

Step-by-step explanation:

To find m/L in triangle ALMN, given that MN = LM and m/M = 45°, we must remember that the sum of angles in a triangle adds up to 180°. Since triangle ALMN has two equal sides (LM and MN), it is an isosceles triangle, which means the angles opposite those sides are also equal. Given that m/M is 45°, m/L must also be 45° to maintain the balance of the isosceles triangle. Therefore, the sum of angles m/L + m/M + m/N = m/L + 45° + m/N = 180°. We know that m/L = 45°, so to find m/N, we calculate 180° - 45° - 45°, which equals 90°.

Thus, m/L is 45°, which corresponds to option A.