Common Issues & FAQs Related to Finding the Interior Angle of a Polygon

Question

Common Issues &#038; FAQs Related to Finding the Interior Angle of a Polygon

Accepted Answer

An interior angle of a polygon is an angle formed by two adjacent sides in the inside of the shape. It can be found by dividing the sum of all the angles in the polygon with the number of sides it has. One way to calculate it is by using a formula, or you can draw out each side and use a protractor or other measuring system to determine its exact size.

Finding interior angles quickly follows some basic concepts that are helpful when calculating any type of geometric shape. First, recognize how many sides there are in the polygon and remember that interior angles always total 360 degrees. For example, for a pentagon (5-sided shape), each individual angle must add up to 360 degrees:

(180 – exterior_angle) * #of_sides = 360

Therefore: (180 – exterior_angle) * 5 = 360

180 – exterior_angle = 72

So once you know the number of sides and what two adjacent angles make up each corner, you can calculate how big each angle must be using this equation and therefore have your answer!

You may also come across situations where you may be given one specific interior angle and not necessarily all of them. Fortunately, finding this one missing piece fits right into what was discussed above. The same process applies here; just subtract your known single angle from 360 and then multiply it times however many sides there are in your polygon:

(360 – known_interior_angle) * #of_sides = Total Degrees

For instance: if you have an octagon where 3 corners were measured at 45° :

(360 – 45°) * 8 = 2160°

Therefore there is 2160° left in our figure which has 8 sections so we divide 2160/8 which gives us our answer 270° per remaining side!