Question

Find the measure of the interior angles of the following regular polygons: a triangle, a quadrilateral, a pentagon, an octagon, a decagon, a 30-gon, a 50-gon, and a 100-gon.

Answer 1

Triangle = 60° ; Quadrilateral = 90° ; Pentagon = 108° ; Octagon = 135° ;

Decagon = 144° ; 30 -gon = 168° ; 50 -gon = 172.8° ; 100 -gon =176.4°

Explanation:

You follow the equation (N-2)*180, then divide the answer with the the number of sides. Example for Triangle: (N-2)*180=(3-2)*180=(1)*180=180 then divide by 3 because in a triangle there are 3 sides. 180/3=60.

Answer 2

Answer with Step-by-step explanation:

Regular polygon: That polygon in which all angles are equal in measure.

Measure of interior angles of polygon=
`((n-2)* 180^(\circ))/(n)`

Where n=Number of sides

1.Triangle:Number of sides=3

Measure of each interior angle=
`((3-2)* 180)/(3)=60^(\circ)`

2.Quadrilateral:Number of sides=4

Measure of each interior angle=
`((4-2)* 180)/(4)=90^(\circ)`

3.Pentagon:Number of sides=5

Measure of each interior angle=
`((5-2)* 180)/(5)=108^(\circ)`

4.Octagon:Number of sides =8

Measure of each interior angle=
`((8-2)* 180)/(8)=135^(\circ)`

5.

Number of sides of decagon=10

Measure of each interior angle=
`((10-2)* 180)/(10)=144^(\circ)`

6.30-gon: Number of sides=30

Measure of each interior angle=
`((30-2)* 180)/(30)=168^(\circ)`

7.50-gon: Number of sides=50

Measure of each interior angle=
`((50-2)* 180)/(50)=172.8^(\circ)`

8.100-gon:

Number of sides=100

Measure of each interior angle=
`((100-2)* 180)/(100)=176.4^(\circ)`