Regular decagon ABCDEFGHIJ rotates 360° counterclockwise about its center. At which angle of rotation does A′ (the image of A) coincide with D?
36°

72°

108°

144°

Question

Regular decagon ABCDEFGHIJ rotates 360° counterclockwise about its center. At which angle of rotation does A′ (the image of A) coincide with D?
36°

72°

108°

144°

anonymous · Answer

help

mathstudent55 · Answer

It's the same as the measure of one interior angle.

anonymous · Answer

so...?

mathstudent55 · Answer

You need to know how to find the measure of an interior angle of a regular polygon.

anonymous · Answer

i will give a medal and fan for the answer

mathstudent55 · Answer

You're going to do better than give a medal.
you're going to solve this problem yourself.
The sum of the measures of the interior angles of a n-sided polygon is 180(n - 2)

mathstudent55 · Answer

If a polygon has n sides, the sum of the measures of its interior angles is 180(n - 2)

mathstudent55 · Answer

In other words, subtract 2 from the number of sides and multiply by 180.
A decagon has 10 sides.
What is 10 - 2 = ?

anonymous · Answer

8

mathstudent55 · Answer

Good.
Now multiply that number by 180.
What do you get?

anonymous · Answer

1440

mathstudent55 · Answer

Since a regular decagon has 10 congruent interiorl angles, the measure of each angle is 1440/10.
What is that?

anonymous · Answer

144

anonymous · Answer

wrong answer

mathstudent55 · Answer

|dw:1426740327531:dw|

mathstudent55 · Answer

Sorry, I misread the problem.
I'll show you now with the figure I drew.

mathstudent55 · Answer

|dw:1426740465097:dw|

mathstudent55 · Answer

|dw:1426740518422:dw|