Answer:
Part 1) For a octagon, the measure of one interior angle is 135 degrees and the measure of one exterior angle is 45 degrees
Part 2) For a icosagon, the measure of one interior angle is 162 degrees and the measure of one exterior angle is 18 degrees
Step-by-step explanation:
Part 1) we have a 8-gon
we know that
A 8-gon or octagon, Is an eight-sided polygon
step 1
The measure of one interior angle in a octagon is equal to
[tex]\frac{180^o(n-2)}{n}[/tex]
where
n is the number of sides of the regular polygon
For n=8
[tex]\frac{180^o(8-2)}{8}=135^o[/tex]
step 2
To find the value of a given exterior angle of a regular polygon, simply divide 360 by the number of sides
so
[tex]\frac{360^o}{8} =45^o[/tex]
Part 2) we have a 20-gon
we know that
A 20-gon or icosagon, Is a twenty-sided polygon
step 1
The measure of one interior angle in a icosagon is equal to
[tex]\frac{180^o(n-2)}{n}[/tex]
where
n is the number of sides of the regular polygon
For n=20
[tex]\frac{180^o(20-2)}{20}=162^o[/tex]
step 2
To find the value of a given exterior angle of a regular polygon, simply divide 360 by the number of sides
so
[tex]\frac{360^o}{20} =18^o[/tex]
