Question

Find the sum of the measures of the interior angles:

Answer 1

The sum of the measures of the interior angles

The sum of interior angles of any polygon can be foud wuth the following general formula

Sum of interior angles = (n-2) \ times 180^{\circ}

where n is the number of sides

1. Nonagon

The Nonagon is a polygon with 9 sides. then,

n = 9

Sum of interior angles of Nonagon

= $(9-2) \times 180^{\circ}$

=$(7) \times 180^{\circ}$

= $1260^{\circ}$

2.Pentagon

The Pentagon is a polygon with 5 sides. then,

n = 5

Sum of interior angles of Pentagon

= $(5-2) \times 180^{\circ}$

=$(3) \times 180^{\circ}$

= $540^{\circ}$

3. 11-gon

The 11-gon is a polygon with 11 sides. then,

n = 11

Sum of interior angles of 11-gon

=$(11-2) \times 180^{\circ}$

=$(9) \times 180^{\circ}$

= $1620^{\circ}$

4. 18-gon

The 18-gon is a polygon with 18 sides. then,

n = 18

Sum of interior angles of 18-gon

=$(18-2) \times 180^{\circ}$

=$(16) \times 180^{\circ}$

=$2880^{\circ}$

5. 38-gon

The 38-gon is a polygon with 38 sides. then,

n = 38

Sum of interior angles of 38-gon

=$(38-2) \times 180^{\circ}$

=$(36) \times 180^{\circ}$

= $6480^{\circ}$

6.56-gon

The 56-gon is a polygon with 56 sides. then,

n = 56

Sum of interior angles 56-gon

=$(56-2) \times 180^{\circ}$

=$(54) \times 180^{\circ}$

=$9720^{\circ}$