Question

Hello mates(◍•ᴗ•◍)❤

The exterior Angle of a polygon is one-third of its interior angle.How many sides does the polygon have?
(WITH FULL EXPLAINATION ONLY)



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Answer 1

Let the interior angle be 3x. Therefore exterior angle is x.

Interior angle + Exterior angle = 180°

because that is a straight line.

So, x + 3x = 180°

4x = 180°

x = 45°

So, exterior angle = 45°

Assuming the polygon is regular, say it had n sides.

We know that sum of all exterior angles is always 360°, so if n sides are there, 45° × n must be equal to 360°

Therefore n = 8.

The polygon has 8 sides!

Answer 2

Step-by-step explanation:

⏩If the interior angle is 3x, the exterior angle is x.

⏩ Hence 3x+x = 4x = 180 or x = 45. The interior angle is 135 deg.

⏩So the polygon has 360/45 = 8 sides or it is a regular octagon.