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As angle M has a measure of 47°, then the measure of angle PNL is 43°
To find: the measure of ∠ PNL .
To proof
As given
∠ M = 47°
In ΔLMN
If the two sides of a triangle are equal and you use the property, the diagonals are also equal.
As given MN = LN
∠ M =∠ L = 47°
and ∠ MPN = 90 °
∠ 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 Measure of angle PNL is 43°.
Hence proved
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