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Based on the calculations, the measure of angle PON (∠PON) in equilateral triangle LMN is equal to 30°.
<h3>What is an equilateral triangle?</h3>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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