Question

12 sides
How many sides does a regular polygon have
if each interior angle is
144
b) 156​

Answer 1

GIVEN:

• interior angle = 144°

FIND:

• no. of sides of polygon.

SOLUTION:

Here, we have

When the regular polygon have if each of its interior angle is 144°. Then the corresponding exterior angle.

$\sf \to144 \degree + x = 180 \degree \: \: \: \: (corresponding \: angle)$

$\sf \to x = 180 \degree - 144 \degree$

$\sf \to x = 36 \degree$

we know, that

The sum of all the exterior angle is 360°

$\sf \longrightarrow so, sides = \frac{360 \degree}{(exterior \: angle)}$

$\sf \longrightarrow sides = \frac{360 \degree}{36 \degree}$

$\sf \longrightarrow sides = \frac{ \cancel{360 \degree}}{ \cancel{36 \degree} } = 10$

$\sf \longrightarrow sides = 10$

Therefore, the no. of sides a regular polygon have is 10.

$\bold{Hence, the\: answer \:will \:be\boxed{ \bold{10 }}}$

Answer 2

Answer:

DATA GIVEN:

EACH INTERIOR ANGLE OF A REGULAR POLYGON IS 144°.

TO FIND:

SIDES OF THE POLYGON.

SOLUTION:

EACH EXTERIOR ANGLE=180-144=36°

NOW SUM OF ALL EXTERIOR ANGLE IS 360°

So SIDES =360°/36°=10 sides.

HENCE THE POLYGON HAS 10 SIDES.