Question

find the magnitude of each of the interior angles of a regular pentagon
octagon
polygon of 12 sides
​

Answer 1

Answer:

We know that the sum of the interior angles of a polygon = (n – 2) π

And each angle of polygon

sum of interior anlgles of polygon/number of sides

(i) Pentagon

Number of sides in pentagon = 5

Sum of interior angles of pentagon = (5 – 2) π = 3π

∴ Each angle of pentagon

3π/5 * 180°/π

(ii) Octagon

Number of sides in octagon = 8

Sum of interior angles of octagon = (8 – 2) π = 6π

∴ Each angle of octagon

5π/7*180/π=900/7=128°34'17''

Answer 2

Answer:

Interior angles of regular polygon is 108 degree, octagon is 135 degree  and polygon of 12 sides is 150 degree

Step-by-step explanation:

Interior angle of regular polygon of n sides is given by

=$\frac{(n-2)180}{n}$

Regular pentagon is having 5 sides, interior angle is

$\frac{(5-2)180}{5} =108^0$

Regular octagon is having 8 sides, interior angle is

$\frac{(8-2)180}{8} =135^0$

Regular polygon of 12 sides , interior angle is

$\frac{(12-2)180}{12} =150^0$

Interior angles of regular polygon is 108 degree, octagon is 135 degree  and polygon of 12 sides is 150 degree