Question

The angles of a regular pentagon are in the ratio 3:5:6:7:9 find all the angles

Answer 1

Let the common ratio be x.

Therefore, the angles of the pentagon would be 3x, 5x, 6x, 7x, and 9x respectively.

Since the sum of all angles in a pentagon is 540 degrees, we can set up the equation:

3x + 5x + 6x + 7x + 9x = 540

30x = 540
x = 18

Therefore, the angles of the regular pentagon are:
3x = 3(18) = 54 degrees
5x = 5(18) = 90 degrees
6x = 6(18) = 108 degrees
7x = 7(18) = 126 degrees
9x = 9(18) = 162 degrees

So, the angles of the regular pentagon are 54 degrees, 90 degrees, 108 degrees, 126 degrees, and 162 degrees.