Supplementary angles
Supplementary angles are two angles whose measures add up to 180 degrees, forming a straight line when placed adjacent to each other. In Grade 6 Saxon Math Course 1 (Chapter 8: Advanced Topics in Geometry and Number Operations), students learn that in a parallelogram, any two consecutive (adjacent) angles are supplementary because the parallel sides create interior angles on the same side of a transversal that sum to 180 degrees. If one angle of a parallelogram measures 65 degrees, the adjacent angle measures 180 - 65 = 115 degrees. Students use this property to find unknown angles in geometric figures.
Key Concepts
Property Remember that supplementary angles have a sum of $180^{\circ}$. In a parallelogram, adjacent angles are supplementary.
Examples An angle of $130^{\circ}$ and an angle of $50^{\circ}$ are supplementary because $130^{\circ} + 50^{\circ} = 180^{\circ}$. In parallelogram $ABCD$, if $\angle A = 80^{\circ}$, then its adjacent angle $\angle B$ must be $180^{\circ} 80^{\circ} = 100^{\circ}$. The supplement of a right angle ($90^{\circ}$) is another right angle ($90^{\circ}$).
Explanation Think of supplementary angles as best buds who always share a straight line, which is a perfect $180^{\circ}$ angle. If one angle takes up some space, its supplement takes up the rest to equal $180^{\circ}$. In a parallelogram, any two neighboring angles are supplementary because the parallel sides force them to share this straight line relationship. They complete each other!
Common Questions
What are supplementary angles?
Supplementary angles are two angles that add up to 180 degrees. They form a straight line when placed next to each other.
If one angle is 72 degrees, what is its supplement?
180 - 72 = 108 degrees.
Why are adjacent angles in a parallelogram supplementary?
The parallel sides of a parallelogram create co-interior angles on the same side of a transversal, which always sum to 180 degrees.
A parallelogram has one angle of 110 degrees. What are the other three angles?
Adjacent angles are supplementary: 180 - 110 = 70 degrees. Opposite angles are equal. So the four angles are 110, 70, 110, 70 degrees.
What is the difference between supplementary and complementary angles?
Supplementary angles sum to 180 degrees. Complementary angles sum to 90 degrees.