Question

Angle M has a measure of 47°.

What is the measure of angle PNL?

43°
47°
86°
94°

Answer 1

The measure of angle PNL = 43

Answer 2

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