5 mistakes learners make with angles in polygons, each one named and explained.
Interior angles come from splitting the polygon into triangles; exterior angles always total 360.
The question asks how many sides and the answer given is an angle, in degrees.
The working really does produce an angle on the way, and it is the last number written down.
Question. Each interior angle is 150 degrees, how many sides
A common answer. 30, which is the exterior angle
The answer. 12
Why. The exterior angle is a step on the way; the number of sides is 360 divided by it.
Check the unit of your answer. A count of sides never has degrees after it.
An exterior angle is given as the interior one, or the two are used in each other's formula.
They sit at the same corner and add to 180, so they are easy to slide between.
Question. Each exterior angle of a regular octagon
A common answer. 135 degrees
The answer. 45 degrees
Why. 135 is the interior angle; the exterior one is what is left of the straight line.
Exterior angles are always the easier calculation: 360 divided by the number of sides.
The size of a single interior angle is given as the sum of all of them, or the reverse.
Both are angle facts about the same polygon and the words sum and angle sit close together.
Question. The sum of the interior angles of a regular pentagon
A common answer. 108 degrees
The answer. 540 degrees
Why. 108 is one of them; there are five, and they total 540.
Check whether the question says each or sum. Those two words do all the work.
The interior angle sum of a hexagon is worked out as 6 x 180, or 5 x 180.
The formula is remembered as sides times 180, because that is most of it.
Question. A hexagon
A common answer. 6 x 180 = 1080
The answer. (6 - 2) x 180 = 720
Why. A hexagon splits into four triangles, not six.
Draw the diagonals from one corner. Count the triangles, and that is what to multiply by 180.
A hexagon is treated as having five sides, so the answer is a pentagon's.
The polygon names are Greek and are not obviously connected to their numbers.
Question. A hexagon
A common answer. (5 - 2) x 180 = 540
The answer. (6 - 2) x 180 = 720
Why. Hex means six, as in hexadecimal or a hexagonal nut.
Learn the prefixes once: penta 5, hexa 6, hepta 7, octa 8. They recur everywhere.
WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.