SOLUTION: The ratio of the angle measures in a parallelogram are 2:3:2:3. Find the measure of the following angles:

Algebra ->  Parallelograms -> SOLUTION: The ratio of the angle measures in a parallelogram are 2:3:2:3. Find the measure of the following angles:      Log On


   

Question 1153977: The ratio of the angle measures in a parallelogram are 2:3:2:3. Find the measure of the following angles:
Answer by ramkikk66(644) About Me  (Show Source):
You can put this solution on YOUR website!


The sum of all the angles of a polygon having n sides (n >= 3) is given by
%282n+-+4%29+%2A+90 degrees.
The sum of all the angles of a parallelogram (which has 4 sides) is
4 * 90 = 360 degrees
The angles are in the ratio 2:3:2:3
So if we assume the first angle is 2x, the other angles are 3x, 2x and 3x. (As you know, opposite angles of a parallelogram are equal)
So sum of the angles -
2x+%2B+3x+%2B+2x+%2B+3x+=+10x+=+360
Solving, x+=+36
Hence the 4 angles are 2x, 3x,2x, 3x i.e.
72 , 108 , 72 and +108+ degrees
Check: Sum = 72 + 108 + 72 + 108 = 360. Confirmed.