Question

Find the meaaure of each interior angle of a regular polygon of 10 sides whise sum of the measure of of the interoir angle is 1250 degree ​

Answer 1

Answer:

The sum of the exterior angles of any regular or irregular polygon, irrespective of the number of sides is 360 degrees.

So each of the exterior angles of a regular 10-sided polygon = 360/10 or 36 deg. Also each of the sides will subtend an angle of 36 deg at the center of the figure. Each interior angle will be 180–36 = 144 deg.

Alternatively, the sum of the interior angles of a regular 10-sided polygon = (n-2)*180 = (10–2)*180 = 8*180 = 1440, so each interior angle = 1440/10 = 144 deg.

Answer 2

Answer:

interior angles in a triangle add up to 180° ...

... and for the square they add up to 360° ...

... because the square can be made from two triangles!

Pentagon

interior angles pentagon

A pentagon has 5 sides, and can be made from three triangles, so you know what ...

... its interior angles add up to 3 × 180° = 540°

And when it is regular (all angles the same), then each angle is 540° / 5 = 108°

(Exercise: make sure each triangle here adds up to 180°, and check that the pentagon's interior angles add up to 540°)