Question

sum of the internal angles of a polygon is 540 degree how many sides does it have if the angles are consecutive natural numbers what is the measure of the smallest angle

Answer 1

Given:

Sum of internal angles = 540°

To Find:

The number of sides and the measure of the smallest angle

Solution:

Let the total number of sides be = x

Therefore,

( x - 2 ) × 180° = 540°

( x - 2) = 540/180

( x - 2) = 3

x = 3 + 2

x = 5

Sicnem It has five sides so it is a pentagon.

Now, the angles are in consecutive order thus,

540/5

= 108°

Therefore -

106° + 107° + 108° + 109° + 110° = 540°

Answer: The sides are five and the smallest angle is 106°