Question

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. The regular pentagon ABCDE rotates counterclockwise about its center to form pentagon A′B′C′D′E′. The angle of rotation at which point A′ coincides with point D is °.

Answer 1

Answer: 144°

Step-by-step explanation:

It is a regular pentagon which means all five sides are the same length. This also means that the angle between any two adjacent vertices is the same. So to find the angle between two adjacent vertices we take 360° and divide it by 5 which equals 72°. But A and D are not adjacent to each other, they have E in the middle (it also has B and C in the middle on the other side, but that's the bigger angle, and we usually label angles through their smaller angle. ex: a 30° angle is 30° if you look at it on the smaller angle (∠ ← here), but if you look at the bigger side of the angle (here →∠) it is 330°, yet we still call it a 30° angle). So, between A and D are two equal angles A to E, and E to D. So we multiply 72° by 2 which equals 144°.

So the answer is 144°.