Question

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Answer 1

Answer:

∠LNM = 38°

∠M  = 52°

Step-by-step 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°