In a parallelogram, one angle is 9 times the size of another. Find the measures of the angles.

In a parallelogram, opposite angles are congruent. However, the same thing cannot be said for the other.

You can label one pair of opposite angles with x and the other 9x.

You also know that each quadrilateral has interior angles that add up to 360 so you can create the equation of

9x+9x+x+x=360

which can be simplified into

20x=360

x=18

Now, you know the angle measures of one pair of opposite angles. to find the other you plug in 18 to our other equation and multiply 9 to get 162.

The angles of the parallelogram is 18,18, 162 and 162.

Note: you can check if this is right if all the angles add up to 360.