Question

1. Find the measure of each angle of a regular octagon.



2. Find the sum of interior angles of a 12 sided convex polygon. Also find the number of diagonals. What can you say about the sum of exterior angle of this polygon?



3. Find the number of sides of regular polygon, each of whose exterior angles measure is 45o.


4. Find the measure of each exterior angle of a regular polygon which has 12 sides.

Answer 1

Answer:

1. 360/8=45°
2. 180(12-2)=1800°
3. 360/45=8 sides
4. 360/12=30°

hope it helps you

Answer 2

1. Find the measure of each angle of a regular octagon.

The measure of each angle = 360°/n

where, n = number of sides of a polygon

360°/8 = 45°

 2. Find the sum of interior angles of a 12 sided convex polygon. Also find the number of diagonals. What can you say about the sum of exterior angle of this polygon?

The sum of interior angles = 180° × (n - 2)

180° × (12 - 2) = 1800°

The sum of exterior angles of any regular polygon = 360°

The number of diagonals of a polygon = n(n - 3)/2

12(12 - 3)/2 = 12(9)/2 = 6(9) = 54

3. Find the number of sides of regular polygon, each of whose exterior angles measure is 45o.

Sum of angles = exterior angle × n

360°/45° = 8 sides

4. Find the measure of each exterior angle of a regular polygon which has 12 sides.

Sum of angles = exterior angle × n

360°/12 = 30°