Question

triangle lmn is an isosceles triangle with $overline{lm}congoverline{ln}$. what is the measure of $angle lmn$?
a. $23^{circ}$
b. $67^{circ}$
c. $46^{circ}$
d. $77^{circ}$

Explanation:

Step1: Identify equal angles

In isosceles △LMN, LM≅LN, so ∠LNM=∠LMN.

Step2: Sum of triangle angles

Total angles = 180°, so ∠LMN + ∠LNM + ∠MLN = 180°.

Step3: Calculate ∠LMN

Let ∠LMN = x, then 2x + 46° = 180°. Solve: 2x = 134°, x = 67°.

Answer:

b. 67°