Answer:
[tex](a)\ Sum = 5760[/tex]
[tex](b)\ \theta = 72[/tex]
[tex](c)\ Sum = 360[/tex]
Step-by-step explanation:
The formulas to each question are given
We have:
(a) Regular 34-gon
Required: The sum of the interior angle
This is calculated as:
[tex]Sum = (n - 2) * 180[/tex]
In this case:
[tex]n = 34[/tex]
So, we have:
[tex]Sum = (34 - 2) * 180[/tex]
[tex]Sum = 32 * 180[/tex]
[tex]Sum = 5760[/tex]
(b) Regular pentagon
Required: Each exterior angle
This is calculated as:
[tex]\theta = \frac{360}{n}[/tex]
In this case:
[tex]n = 5[/tex] --- sides of a pentagon
So, we have:
[tex]\theta = \frac{360}{5}[/tex]
[tex]\theta = 72[/tex]
Solving (c): 72-gon
Required: Sum of exterior angles
This is calculated as:
[tex]Sum = 360[/tex]
