Question

How many degrees are in each interior angle of a regular pentagon? 50 72 108 120

Answer 1

The answer 108 degrees.

Answer 2

Answer: $108^{\circ}$

Step-by-step explanation:

The sum of all the angles in a regular polygon with sides n , is given by :-

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

Now, the sum of all the angles in a regular pentagon with 5 sides will be :-

$S_5=180^{\circ}(5-2)=180^{\circ}(3)=540^{\circ}$

We know that all the interior angles of a regular polygon are equal .

Therefore, the measure of each interior angle in a pentagon is given by :-

$x=\dfrac{540^{\circ}}{5}=108^{\circ}$

Hence, the measure of each interior angle in a pentagon=$108^{\circ}$