Question

Find the measure of each interior angle a polygon of side 15​

Answer 1

Answer :-

The measure of each interior angle of a polygon of side 15 is 156°.

Step-by-step explanation

To Find :-

• The measure of interior angle of polygon.

★ Solution

Given that,

• Total number of sides = 15 sides.

ㅤㅤㅤㅤㅤㅤ_____________________

ㅤㅤㅤ✧ㅤMethod 1 :-

As we know that,

The sum of interior angles of polygon is (n-2)180°

Where,

• n = side.

→ (n - 2) × 180

→ (15 - 2) × 180

→ 13 × 180

→ 2340 = sum of interior angles.

∴ One interior angle :-

→ 2340/n

→ 2340/15

→ 156° = Interior angle

Hence, The Interior angle is 156°.

ㅤㅤㅤ✧ㅤMethod 2 :-

By using the formula,

Interior angle of polygon = (n - 2)180/n,

Where,

• n = side

According the question,

→ (n - 2)180/n

→ (15 - 2)180/15

→ 13*180/15

→ 2340/15

→ 156° = Interior angle

Hence, The interior angle = 156°

Answer 2

Answer:

$\green{ \boxed{ \bf \: The \: each\: interior \: angle \: = 156°}}$

Step-by-step explanation:

Given,

• A polygon has 15 sides.

We have to find :

• Each interior angle of the polygon.

Solution :

We know that

$\bf \: Interior \: angle \: of \: polygon \: = \frac{(n - 2) \times 180}{n}$

→ n denotes side

According the question,

n = 15

Now,

$\bf \: Interior \: angle = \frac{(15 - 2) \times 180}{15} \\ = \frac{13 \times 180}{15} \\ = \frac{2340}{15} \\ = \green{ {156}^{ \circ} }$

So,

The interior angle = 156°