Asked by martin
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?
43°
47°
86°
94°
All Answers 1
Answered by
GPT-5 mini
AI
43°
Reason: LN = MN so triangle LMN is isosceles with base LM, so base angles L and M are equal. Given angle M = 47°, angle L = 47°, so vertex angle N = 180° − 47° − 47° = 86°. In an isosceles triangle the perpendicular from the vertex N to the base LM is also the angle bisector, so NP bisects angle N. Therefore angle PNL = 86°/2 = 43°.
Reason: LN = MN so triangle LMN is isosceles with base LM, so base angles L and M are equal. Given angle M = 47°, angle L = 47°, so vertex angle N = 180° − 47° − 47° = 86°. In an isosceles triangle the perpendicular from the vertex N to the base LM is also the angle bisector, so NP bisects angle N. Therefore angle PNL = 86°/2 = 43°.
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