Question

Triangle lmn is an isosceles triangle with lm = ln. What is the measure of angle lmn?

1) 46 degrees
2) 67 degrees
3) 90 degrees
4) Cannot be determined

Answer 1

The measure of angle LMN in an isosceles triangle with LM = LN is 60 degrees.

Step-by-step explanation:

An isosceles triangle has two sides that are equal in length. In triangle LMN, if LM = LN, then it is an isosceles triangle. In an isosceles triangle, the angles opposite the equal sides are also equal. Therefore, the measure of angle LMN is the same as the measure of angle LNM.

Since the three angles of a triangle add up to 180 degrees, we can assume that angle LNM + angle LMN + angle MNL = 180 degrees. Since angle LNM = angle LMN, we can rewrite the equation as 2 * angle LMN + angle MNL = 180 degrees. Since angle MNL is the same as angle LMN, we can rewrite the equation as 2 * angle LMN + angle LMN = 180 degrees. Simplifying further, we get 3 * angle LMN = 180 degrees. Dividing both sides by 3, we find that angle LMN = 60 degrees.