Question

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

Answer 1

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.