Question

Angle M has a measure of 47°. Triangle L M N is cut by perpendicular bisector N P. The lengths of sides L N and N M are congruent. Line segments L P and P M are congruent. Angle P M N is 47 degrees. What is the measure of angle PNL? a. 43° b. 47° c. 86° d. 94°

Answer 1

The answer is 43

Explanation:

I took the test

Answer 2

The correct option is a. 43°

Explanation:

In triangle LMN,

NP is perpendicular bisector, i.e. LP = PM and m∠NPM = m∠NPL = 90°,

Also, LN = NM,

Since, the sum of all interior angles of a triangle is 180°,

∴ m∠NPM + m∠NMP + m∠MNP = 180°

We have,

m∠NMP = 47° ( given ),

90° + 47° + m∠MNP = 180°

137° + m∠MNP = 180°

m∠MNP = 180° - 137° = 43°,

Now, in triangles NLP and NMP,

LP = PM,

LN = NM,

PN = PN,

By SSS postulate of congruence,

Δ NLP ≅ Δ NMP

By CPCTC,

m∠PNL = m∠MNP

⇒ m∠PNL = 43°

Hence, OPTION a. is correct.