Question

The external angle of a regular polygon is 20degree. How many sides does it have? What is the total measure of its angles

Answer 1

Answer:

The exterior angle of a regular polygon is 20 degree. How many sides does it have? What is the measure of each interior angle? What is the total measure of its angles?

Answer

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

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°

Answer 2

QUESTION -

The external angle of a regular polygon is 20degree. How many sides does it have? What is the total measure of its angles?

ANSWER -

Let the number of sides of a regular polygon are n, its each exterior angle = 360°/n.

Accordingly :-

360°/n = 20°. => n = 360°/20° = 18 sides.

We know that:-

each interior angle + each exterior angle = 180°

each interior angle + 20° = 180°.

or, each interior angle =180° -20° = 160°.

Sum of all interior angles= 18×160° = 2880°.

Sum of all exterior angles = 18×20° = 360°

Sum of all the interior angles and all exterior angles= 2880°+360°= 3240° , 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.