How do you work out interior and exterior angles?

Answer 1

INTERIOR ANGLES

OK, here's a geometry lesson for you. This rule works for shapes with any amount of sides, as long as they are equilateral (all sides and angles the same).

All the interior (inside) angles follow a linear sequence of adding 180, starting with a triangle (3 sides) adding up to 180, a square (4 sides) adding up to 360, a pentagon (5 sides) adding up to 540, a hexagon (6 sides) adding up to 720 etc.

So, for example, to work out the interior angles of a Hendecagon (11 sides) It would be 180 + 180 + 180 + 180 + 180 + 180 + 180 + 180 + 180 (or 180 x 9) = 1620. REMEMBER to subtract 2 from the number of angles THEN multiply by 180. This may sound confusing, but it is because this doesn't work for 1 and 2 sided shapes. That is why, in the Hendecagon (11 sides) example, it was 180 x 9.

Now to work out the angles. In many cases it could be easier just to learn them, (trianlge, 60, square, 90 etc etc etc) but, again, you can still work out what you don't know. Lets take our friend the Hendecagon (11 sides). As before, 9 x 180 = 1620. You then simply divide this number by the original number (before you subtracted 2) So, 1620 divided by 11 = 147.2727272727 (rounded to 147.3). So, the INTERIOR angle of a Hendecagon is 147.3o

EXTERIOR (out side) ANGLES:Once you know the INTERIOR ANGLE, working out the exterior is EASY! 360 minus Interior = Exterior. So, with our Hendecagon, 360 minus 147.3 = 212.7.

Summary - Number of sides (11) minus 2 (9) x 180 (1620) divided by original number (11) equals INTERIOR ANGLE (147.3)

360 - INTERIOR ANGLE (147.3) equals EXTERIOR ANGLE (212.7)

Remember to write the o symbol!

How do you work out interior and exterior angles