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

The parallelogram angle alpha and beta form 180 degrees (angles on one basis). α + β = 180 β = 9 α 9 α + α = 180 10 α = 180∣ : 10 α = 18 β = 180 − 18 = 162

Answered by MattD | 2024-06-10

To find the angle measures in a parallelogram where one angle is nine times the size of another, we have to use the property that in a parallelogram, opposite angles are equal and the sum of adjacent angles is 180 degrees. Let the smaller angle be x degrees. Then the larger angle is 9x degrees because it is nine times the smaller angle.
Since the angles are adjacent in a parallelogram, their sum must be 180 degrees, so we set up an equation:
x + 9x = 180
Solving this, we combine like terms to get 10x = 180, and then divide both sides by 10 to find that x = 18 degrees. Therefore, the smaller angle is 18 degrees and the larger angle is 9 times 18, which is 162 degrees.
Finally, since opposite angles are equal in a parallelogram, there are two angles of 18 degrees and two angles of 162 degrees in the parallelogram.

Answered by NetaLeeHershlag | 2024-06-24

In a parallelogram where one angle is nine times another, the smaller angle is 18 degrees while the larger angle is 162 degrees. This leads to two angles of 18 degrees and two angles of 162 degrees in total. The relationship stems from the property that adjacent angles in a parallelogram add up to 180 degrees.
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Answered by NetaLeeHershlag | 2024-12-24