Question

in a regular polygon, each interior angle is thrice the exterior angle. find the number of sides of the polygon.

pls hlpppppp

Answer 1

Let the Exterior angle be a

Interior angle = 3a

We know that,

Exterior angle + Interior angle = 180

=> a + 3a = 180

=> 4a = 180

=> a = 45°

Interior angle = 3 × 45 = 135°

Exterior angle = 45°

Now,

n × Each Exterior angle = 360

=> n × 45 = 360

=> n = 8

Number of sides = 8

Answer 2

Answer:

8 sides

Step-by-step explanation:

The sum of the interior and exterior angles must be 180 deg.

Let x = the measure of the exterior angle

Then x + 3x = 180 -> 4x = 180 -> x = 45

The exterior angles of a regular polygon add up to 360, which means each exterior angle is 360/n [n=number of sides]

So we have 360/n = 45 -> n = 360/45 = 8

So the polygon is an octagon (8 sides)

HOPE THIS WILL HELPS YOU

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