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

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)`