Find the angles of a regular five point star? - Answers

today i took my grade 9 EQAO math test and this was a question on it, the hardest on the test it gave me a picture of a five point star (drawn as you would without lifting the pecnil, with five lines). I had to solve for angles abcde (the angles within the point of the star) withough a protractor, and no measurements given. impossible you may say, but there is a sure way that is the same for a star of any size first thing you must realize is that when you draw a star, a pentagon is formed in the middle, with 5 isoscles triangles off each side. step 1: find the angle of each side of the pentagon if you didn't already know, the formula for finding each angle of a regular shape is, with n being the number of sides in the shape is: 180(n - 2) / n. Of course if you plug in 5 that will make 180(3) / 5, 540 / 5, so 108 degrees. step 2: fromm that find two of the three angles of each triangle in the star it can be done quite easily. looking at any of the five lines, you could, and this isn't easy to explain withough pictures, but on any of the lines you will see 108 degress, and it is clear that the total between that angle and the base angles in the triangle add up to 180. So each of the base angle sof the triangle are 72 degress. draw it and it will be clear sorry i can't explain this well. step 3: find the third angle of the triangle you should know how to do this. the three angles of a triangle add up to 180 always so u subtract the two known angles from 180 to find the third. since 180 - 72 - 72 = 36, that is the angle of each point. so, angles abcde (which must be equal) = 36 degrees