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

Answer

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

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

Step-by-step 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=$\frac{(n-2)\times 180^{\circ}}{n}$

Where n=Number of sides

1.Triangle:Number of sides=3

Measure of each interior angle=$\frac{(3-2)\times 180}{3}=60^{\circ}$

2.Quadrilateral:Number of sides=4

Measure of  each interior angle=$\frac{(4-2)\times 180}{4}=90^{\circ}$

3.Pentagon:Number of sides=5

Measure of  each interior angle=$\frac{(5-2)\times 180}{5}=108^{\circ}$

4.Octagon:Number of sides =8

Measure of  each interior angle=$\frac{(8-2)\times 180}{8}=135^{\circ}$

5.

Number of sides of decagon=10

Measure of  each interior angle=$\frac{(10-2)\times 180}{10}=144^{\circ}$

6.30-gon: Number of sides=30

Measure of  each interior angle=$\frac{(30-2)\times 180}{30}=168^{\circ}$

7.50-gon: Number of sides=50

Measure of  each interior angle=$\frac{(50-2)\times 180}{50}=172.8^{\circ}$

8.100-gon:

Number of sides=100

Measure of  each interior angle=$\frac{(100-2)\times 180}{100}=176.4^{\circ}$