Question

in the figure m angle PNM =75 degree , what is m angle PLN ?
1.75 2.60 3.65 4.70​
answer fast

Answer 1

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

$x+x+90=180$

$2x=180-90=90$

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

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

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

$120+\angle PLN=180$

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

m angle PLN=60 degree

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