Question

10. If the sum of interior angles of a polygon is 3780°, find the number of sides.

12. An exterior angle of a regular polygon is one-fourth of its interior angle. Find the number of
sides in the polygon.​

Answer 1

Answer:

Answer. therefore no. of sides are 22 .

Answer 2

Q12. An exterior angle of a regular polygon is one-fourth of its interior angle. Find the number of sides in the polygon.

Let x be the exterior angle of a regular polygon and y be the corresponding interior angle of a polygon.

Given that exterior angle is one fourth of its interior angle.

⇒x=4y     ...(1)

Since x and y are exterior and corresponding interior angles, we have,

x+y=180∘

⇒4y+y=180∘

⇒45y=180∘

⇒y=5180∘×4=144∘

⇒x=180∘−y=180∘−144∘=36∘

If each exterior angle of a regular polygon is A∘ then the number of sides in the polygon=A360∘

Since exterior angle is 36∘, the number of sides in the polygon=36∘360∘=10

10. If the sum of interior angles of a polygon is 3780°, find the number of sides.

To calculate the sum of interior angles of a polygon having 'n' sides, we use (n-2) 180°, where n = number of sides

So, (n-2) 180° = 3780°

=> n - 2 = 21

So, n = 21 + 2 = 23 sides

Therefore, If the sum of interior angles of a polygon is 3780°, then the number of sides will be 23.