Each interior angle of a regular polygon is 140°.Find the number of sides of the polygon.

Answer :

9 sides

Explanation:

Step 1

Since the interior angle is 140 degrees, the supplement of this is the exterior angle and equal to 40 degrees. Hence the number of sides is 360/40 = 9 sides.

Step 2

Method 2: Since the exterior angle is 140°

The sum of the interior angles = (2n - 4) × right angles.

So 140n =(2n - 4) ×right angles, or we can also say

140n =(2n - 4) × 90

140n = 180n - 360

40n = 360

Divide both sides of the equation by 40

n = 9 sides.

n = 9 sides.Hence the number of sides is 9 sides.

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.

what?

step-by-step explanation:

what do you need with. i love quadrants. can you tell me ?