Question

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Answer 1

∠LNM = 38°

∠M = 52°

Explanation:

Here, ∠M = x

Let the measure of ∠LNM = ∠1

Now, ∠PNM + ∠1 = 180° (LINEAR PAIRS)

So, ∠1 = 180° - ∠PNM = 180° - 142°

= 38°

⇒∠1 = 38° , or ∠LNM = 38°

Now, in triangle LMN, by ANGLE SUM PROPERTY of a triangle

∠NLM + ∠X + ∠1 = 180°

or, 90° + x + 38° = 180°

⇒ x = 180° - 128° = 52°

Hence, the measure of x = 52° , or ∠M = 52°