Answer:
Internal angle = [tex]160^\circ[/tex]
Number of sides = 18
Step-by-step explanation:
Given that:
We have a regular polygon with number of sides unknown.
Measure of an exterior angle of the polygon = [tex]20^\circ[/tex]
To find:
Measure of an interior angle and the number of sides of the polygon?
Solution:
Let us have a look at the relation of sum of external angles.
Sum of one internal angle and its corresponding external angle = [tex]180^\circ[/tex]
Internal angle + external angle = [tex]180^\circ[/tex]
Internal angle = [tex]180^\circ[/tex] - [tex]20^\circ[/tex] = [tex]160^\circ[/tex]
Sum of all the external of a regular polygon = [tex]360^\circ[/tex]
All the external angles will be equal because it is a regular polygon.
Let the number of sides = [tex]n[/tex]
Therefore,
[tex]n \times 20^\circ = 360^\circ\\\Rightarrow n = 18[/tex]
Therefore, the answers are:
Internal angle = [tex]160^\circ[/tex]
Number of sides = 18
