Answer:
The correct option is a. 43°
Step-by-step 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.
