Question

Find the value of N, P and M

Answer 1

N = 80 degrees
P = 95 degrees
M = 95 degrees

N and 100 form a 180 degree angle and thus you can solve using subtraction.

P is the same angle as the angle opposite of it. 

You can get M by subtracting the other 3 angles from 360.

Answer 2

Answer:

A linear pair is two angles that are adjacent to each other and forms a line.

Supplementary Angle: If any two angles form a linear pair, then they are supplementary(i.e, 180 degree).

From the  given figure, $100^{\circ}$ and $n^{\circ}$ forms a linear pair.

Also, if the two angles are linear pair, then they are supplementary angle.

then,

$100^{\circ}+n^{\circ}=180^{\circ}$  

Simplify:

$n = 180-100=80^{\circ}$

Vertical opposite angle theorems states about the two angles that are opposite to each other and are equal also.

From the figure, $p^{\circ}$ and $95^{\circ}$ are vertical opposite angle.

therefore, $p=95^{\circ}$

Now, to find the value of m;

Sum of the measures of the interior angles of a polygon with 4 sides is 360. degree.

here, $n^{\circ}$, $p^{\circ}$ , $m^{\circ}$ and $90^{\circ}$ forms a qudrilateral.

therefore, by definition:

$n^{\circ}+p^{\circ}+m^{\circ}+90^{\circ}=360^{\circ}$

Substituting the values of $p=95^{\circ}$ and $n=80^{\circ}$ we have;

$80+95+m^{\circ}+90^{\circ} = 360^{\circ}$ or

$265^{\circ}+m^{\circ}=360^{\circ}$

Simplify:

$m^{\circ}=360^{\circ}-265^{\circ}=95^{\circ}$

Therefore, the value of $n=80^{\circ}$ , $p=95^{\circ}$ and $m=95^{\circ}$