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.





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Answer 1

Answer:

Step-by-step explanation:

1. No.of sides=8

We know sumo f the internal angles is (n-2) x 180

So ,

(8-2) x 180=6 x 180= 1080°

Therefore each side measuring 1080/8=135°

2.  sumof the interior angles = (n-2) x 180=12-2 x 180=10 x 180=1800°

No.of diagonals=n(n-3) /2=12( 12-3)/2=108/2=54

3. Exterior angle measure=45degree

360/exterior angle measure=no.of sides

so

360/45=8 sides

4. Each exterior angle= 360/no.of sides

360/12=30°

Hope it is helpful

BRAINLIEZT  plz

Answer 2

Answer:

1. measure of each angle of regular octagon

= ( n -2 ) × 180°

= ( 8 - 2 ) × 180°

= 6 × 180°

= 1080°

3. Total measure of all exterior angle = 360°

Measure of each exterior angle = 45°

Therefore, the number of exterior angles

= ( 360°/n ) = ( 360°/45°)

= 8

The polygon has 8 sides

4. Each exterior angle of regular polygon

= (360°/n) = (360°/12)

= 30°