Question

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?​

Answer 1

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 2

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