Question

Find each angle of a 24-sided regular polygon? Find each outer angle and sum of interior angle

Answer 1

Each outer angle is 15°

The sum of interior angles is 3960°

Explanation:

The given polygon has 24 sides.

Now, we shall determine the angle of each outer angle.

Each outer angle can be determined using the formula,

$\frac{360}{n}$

where n is the number of sides. Here $n=24$

Substituting in $\frac{360}{n}$ , we have,

$\frac{360}{24}=15^{\circ}$

Thus, the angle of each outer angle is 15°

The sum of interior angle can be determined using the formula,

$Sum=(n-2) 180^{\circ}$

$Sum=(24-2) 180^{\circ}$

$Sum=(22) 180^{\circ}$

$Sum=3960^{\circ}$

Thus, the sum of the interior angle is 3960°