Question

find the sum of interior angles of polygon of given number of sides by using formula (n-2) × 180°​

Answer 1

Answer:

1) 1800°

2) 1260°

3) 3600°

Step-by-step explanation:

1) given sides= 12

Sum of all angles in a polygon= (n-2) × 180°

                                                  = (12-2) × 180°

                                                  = 10× 180°= 1800°

2) given sides= 9

Sum of all angles in a polygon= (n-2) × 180°

                                                  = (9-2) × 180°

                                                  = 7× 180°= 1260°

3) given sides= 22

Sum of all angles in a polygon= (n-2) × 180°

                                                  = (22-2) × 180°

                                                  = 20× 180°= 3600°

Answer 2

Answer:

• i = 1800

• ii = 1260

• iii = 3600

Solution :

By the formulae : ( n - 2 ) × 180°

• n = sides

i ) 12 sides

⟶ n = 12

⟶ ( 12 - 2 ) × 180

⟶ 10 × 180

⟶ 1800

∴ The sum of interior angles of this polygon is 1800.

ii ) 9 sides

⟶ n = 9

⟶ ( 9 - 2 ) × 180

⟶ 7 × 180

⟶ 1260

∴ The sum of interior angles is 1260.

iii ) 22 sides

⟶ n = 22

⟶ ( 22 - 2 ) × 180

⟶ 20 × 180

⟶ 3600

∴ The sum of interior angles is 3600.

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★Learn More :

• ) The Sum of the angles of an n - sided polygon is ( n - 2 ) × 180°.

• ) The sum of the angles of any polygon is a multiple of 180°.

• ) If an n - sided polygon is divided into n triangle . Thus sum of all the angles is n × 180°.

• ) The sum of the outer angles of any polygon is 360°.

• ) The sum of outer angles is n × 180° - ( n - 2 ) × 180°.