Question

In the figure below, ∆LMN is an equilateral triangle, side \overline {LM} LM is bisected by O, side \overline {LN} LM is bisected by P, and \overline {ON} ON bisects \angle LNM∠LNM . What is the degree measure of \angle PON∠PON ?

Answer 1

Based on the calculations, the measure of angle PON (∠PON) in equilateral triangle LMN is equal to 30°.

What is an equilateral triangle?

An equilateral triangle can be defined as a special type of triangle that has equal side lengths and all of its three (3) interior angles are equal.

Since triangle LMN is an equilateral triangle, the following applies:

LN = LM = MN

∠LNM = ∠L = ∠LM = 60°

OP // MN (O and P are midpoint).

∠NPO = 90° + (90° - 60°) = 120°

∠PNO = ∠LNP/2 = 60/2 = 30°.

Therefore, ∠PON is given by:

∠PON = 180° - (∠PNO + ∠NPO)

∠PON = 180° - (30° + 120°)

∠PON = 180° - 150°

∠PON = 30°

Read more on equilateral triangle here: brainly.com/question/14709905

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