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Hitman42 [59]
4 years ago
9

Find the value of N, P and M

Mathematics
2 answers:
Ket [755]4 years ago
8 0
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.
joja [24]4 years ago
3 0

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}

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