Question

sum of all interior angles of a pentagon tell me full sum​

Answer 1

Answer:

Sum of all the interior angles of a polygon = (n – 2)π, where n is the number of side in the polygon.

Answer 2

Step-by-step explanation:

Now, we have to find the sum of the interior angles of a pentagon.

We know that the sum of interior angles ‘A’ of any polygon of sides ‘n’ is given by the formula 

A=(n−2)×180∘

Thus, we will use this formula to find the required sum.

We know that a pentagon has 5 sides. Thus,

 n=5n=5.

Putting the value of ‘n’ in the formula, we get

A=(n−2)×180∘

⇒A=(5−2)×180∘

⇒A=3×180∘

⇒A=540∘

Thus, the sum of interior angles of a pentagon is 540∘

Now, let us find out the measure of each angle in a regular pentagon.

We can find it through the following method:

We will divide the sum of the measures of the angles by the number of sides of the polygon.

Sum of the measure of the angles of a pentagon=540∘

No. of sides in a pentagon= 5

Thus, measure of one angle of a regular pentagon is give as:

 540∘5⇒108∘

Therefore, the measure of one angle of a regular pentagon is 108°.

We can verify it by multiplying 108° by 5.

108∘×5=540∘

But this can only be calculated if the polygon is regular, i.e. we can only find the measure of one angle of a pentagon if the pentagon is a regular one, i.e., all of its sides are of the equal length.

Thus, the required answer is 540∘