Each exterior angle of a regular polygon is 20° . How many sides are there in the
polygon? What is the measure of each interior angle of the regular polygon?
Answers
Answer:
Sides
Since the sum of the exterior angles of a polygon is 360° and an angle of the regular polygon is 20°, then 360° / 20° is the number of sides. Let the number of sides be n.
n = 18, an octadecagon.
Measure of Each Interior Angle
If you imagine a regular octadecagon (or any polygon), you will notice that the exterior angle is the supplement of the interior angle.
20° = 180° - I, where I is the interior angle.
[20°] + I = [180° -I] + I
[20° + I] - 20° = [180°] - 20°
I = 160°
Total Measure of its Angles
I am not sure what this meant, but I’m assuming that this is the sum of the interior angles and the exterior angles.
Sum of the Interior Angles
Sum of interior angles is 180° (n - 2). The way I remember this equation is by remembering that the equation contains 180° and the number of sides, and that the sum of interior angles of a triangle is 180°.
180° (18 - 2)
180° (16)
(200 - 20)° (16)
(3200 - 320)°
2880°
Can also find the sum by multiplying I by n
160° * 18
160° * (20 - 2)
3200° - 320°
2880°
Sum of the Exterior and Interior angles
360° + 2880° = 3240°
Step-by-step explanation:
pls mark as branliest
Answer:
18
Step-by-step explanation:
Exterior angle - 20
no. of exterior angles = no. of sides
(because there is a exterior angle on every side)
Sum of all exterior angles= 360
Therefore,
no. of sides= 360 ÷20
= 18