Question 15. Five identical right angled triangles can be arranged so that their larger acute angles touch to form the star shown in the diagram. It is also possible to form a different star by arranging more of these triangles so that their smaller acute angles touch. How many triangles are needed to form the second star? We take a closer look at the triangle. We know that it is our right triangle, so one of the corners will be 90 degrees. To find how many degrees the larger acute angle is, we simply have to do 360 divided by 5. With this we get 72, so that the larger acute angle is 72. We know that on any given triangle, the total sum of all of the angles is 180. So if we subtract 90 and 72, we get 18. So the smaller acute angle is 18. Now to find how many triangles are needed to form a star with smaller acute angles, we simply do 360 divided by 18, and this gives us our answer, 20. So the answer is D, 20.

right angled triangles

larger acute angles

smaller acute angles

star formation

geometry problem