Question

in a regular polygon, one of its inner angle is 3 times outer angle?
a) what is the sum of inner and outer angle of any polygon? b) how many sides are there for this polygon?​

Answer 1

Given,

Inner angle = 3× outer angle

To find,

• The sum of inner and outer angle of any polygon.
• Number of sides of the given polygon.

Solution,

Now, an inner angle and an outer angle lies on the same straight line. That's why, the sum of any inner angle and outer angle of any polygon will be 180°.

Let, the outer angle = x

Inner angle = 3x

x+3x = 180

4x = 180

x = 45°

Inner angle = (3×45°) = 135°

Let, the number of sides of the polygon = n

Now,

180(n-2)/n = 135

180n-360 = 135n

180n-135n = 360

45n = 360

n = 8

Hence, the sum of the internal angle and external angle of a polygon is 180° and the number of sides of the given polygon is 8.