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 with Step-by-step explanation:
Regular polygon: That polygon in which all angles are equal in measure.
Measure of interior angles of polygon=[tex]\frac{(n-2)\times 180^{\circ}}{n}[/tex]
Where n=Number of sides
1.Triangle:Number of sides=3
Measure of each interior angle=[tex]\frac{(3-2)\times 180}{3}=60^{\circ}[/tex]
2.Quadrilateral:Number of sides=4
Measure of each interior angle=[tex]\frac{(4-2)\times 180}{4}=90^{\circ}[/tex]
3.Pentagon:Number of sides=5
Measure of each interior angle=[tex]\frac{(5-2)\times 180}{5}=108^{\circ}[/tex]
4.Octagon:Number of sides =8
Measure of each interior angle=[tex]\frac{(8-2)\times 180}{8}=135^{\circ}[/tex]
5.
Number of sides of decagon=10
Measure of each interior angle=[tex]\frac{(10-2)\times 180}{10}=144^{\circ}[/tex]
6.30-gon: Number of sides=30
Measure of each interior angle=[tex]\frac{(30-2)\times 180}{30}=168^{\circ}[/tex]
7.50-gon: Number of sides=50
Measure of each interior angle=[tex]\frac{(50-2)\times 180}{50}=172.8^{\circ}[/tex]
8.100-gon:
Number of sides=100
Measure of each interior angle=[tex]\frac{(100-2)\times 180}{100}=176.4^{\circ}[/tex]
