Question

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

Answer 1

The parallelogram angle alpha and beta form 180 degrees (angles on one basis).

`\alpha+\beta=180`

`\beta=9\alpha`

`9\alpha+\alpha=180`

`10\alpha=180|:10`

`\alpha=18`

`\beta=180-18=162`

Answer 2

If you pick any two angles out of a parallelogram, either they're equal, or else they add up to 180 degrees.

Call the smaller angle 'A'. Then the bigger one is '9A' .
Their sum is 180 degrees.

10A = 180

Divide each side by 10 :

A = 18

One angle is 18 degrees.
The other one is 9 x 18 = 162 degrees.