Maths 9-1 Higher Tier QuestionWatch
Tip: Use (180(n - 2) )divided by n
Exterior angle of a 12 sided shape is 30 degrees since 360/12= 30. If you draw this on the diagram you will see that this angle can go through a square. The angle in a square is 90 so (90-30) = 60 degrees. Angles in a straight line sum 180 so 180-60 = 120. Interior angles of a regular hexagon are 120. Rearrange the formula 120= 180(n-2)/n to prove this. (You’ll get n=6) I hope this helps let me know if you don’t understand any of it
Then do 180 - interior angle = exterior angle of polygon.
Then find the number of sides by doing:
number of sides = 360 divided by exterior angle.
So one interior angle of regular polygon = (180 x (n-2)) divided by n.
Find interior angles for square and 12 sided polygon using formula.
Do 360 - interior angle of square - interior of 12 sided polygon to find interior of your polygon, p. (360 around a point).
Do 180 - interior angle to find exterior angle.
Divide 360 by exterior angle to find number of sides.
If number of sides = 6 the shape is a hexagon, proof complete.