Answer
Find out the measure of ∠ PNL .
To proof
As given
∠ M = 47°
In ΔLMN
Now by using the property if two sides of a triangles are equal than their opposite angles are also equal .
As given MN = LN
∠ M =∠ L = 47°
and ∠ MPN = 90 °
(As shown in the diagram)
∠ MPN + ∠ NPL = 180° (Linear pair)
∠ NPL = 180° - 90°
∠ NPL = 90°
Now by using the angle sum property of a triangles
in Δ NPL
∠NPL +∠PNL + ∠NLP = 180°
90 + 47 + ∠PNL = 180
137+ ∠PNL = 180
∠PNL = 180 - 137
∠PNL = 43 °
therefor the option (A) is correct .
Hence proved
