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.
please tell with step by step
Answers
Answer:
Step-by-step explanation:
1)In a regular octagon, each angle measures 135 degrees. Subtract two from the number of sides in an octagon. Since an octagon has eight sides, subtract two from eight to get six. Multiply six by 180 to find the total number of degrees in an octagon equals 1,080. Add the angle measures of the seven known angles to find the sum of those angles.
2)To find the sum of the interior angles of a convex 12-sided polygon, you use the formula (n-2)180 n being the number of sides Therefore, (12-2)180 = 10(180) = 1800 degrees So the sum is 1800 degrees I believe this is right, but please correct me if I am wrong.
3)Total measure of ext. angles=360
Measure of each=45
NO. of sides=360/45=8
Therefore,the answer is 8
4)For all polygons, the sum of all exterior angles adds up to 360 degrees. For each vertex, the interior angle plus the exterior angle = 180 degrees, so if a regular pentagon has 12 sides, then for all 12 exterior angles to add up to 360 degrees each one must be 30 degrees. Therefore the interior angle is 180 degrees minus 30 degrees = 150 degrees.