Question

In the figure, m<PNM=75°. What is m <PLN?

1)75°
2)60°
3)65°
4)70°

show in solving step by step​

Answer 1

Answer:

m angle PLN=60 degree

Step-by-step explanation:

In triangle PNM=75 degree

ML=MN

Angle made by equal sides are equal

Angle MNL=Angle MLN

Let angle MLN=x

In triangle MLN

Angle LMN=Angle LPN=90 degree (Angle subtended by half circle=90 degree)

Where LN is a diameter of circle

Angle MLN+angle MNL+angle LMN=180 degree

By using triangle angles sum property

Substitute the values

x+x+90=180x+x+90=180

2x=180-90=902x=180−90=90

x=\frac{90}{2}=45^{\circ}x=

2

90

=45

∘

Angle MNL=x

Angle PNL=Angle PNM-angle MNL=75-45=30 degree

In triangle LPN

Angle LPN+angle LNP+angle PLN=180 degree

Substitute the values

30+90+\angle PLN=180^{\circ}30+90+∠PLN=180

∘

120+\angle PLN=180120+∠PLN=180

\angle PLN=180-120=60^{\circ}∠PLN=180−120=60

∘

m angle PLN=60 degree

Step-by-step explanation:

With regards

Nami