Angles of a parallelogram
The angles of a parallelogram follow two rules: opposite angles are equal, and consecutive (adjacent) angles are supplementary, meaning they add up to 180 degrees. If one angle of a parallelogram measures 70 degrees, the opposite angle is also 70 degrees, and both adjacent angles are 180 - 70 = 110 degrees. All four angles always sum to 360 degrees. This 7th grade geometry skill from Saxon Math Course 2 connects angle relationships to quadrilateral properties and supports all future work with polygons.
Key Concepts
Property 1. Nonadjacent angles (in opposite corners) have equal measures. 2. Adjacent angles (sharing a side) are supplementary, meaning their sum is $180^\circ$.
Examples If one angle is $110^\circ$, its opposite is also $110^\circ$. The other two angles are each $180^\circ 110^\circ = 70^\circ$. In a parallelogram with a $75^\circ$ angle, the adjacent angles are $105^\circ$, and the opposite angle is $75^\circ$.
Explanation When you squish a rectangle, angles in opposite corners stay twins, always having the same measure. Any two neighbors, however, become partners that always add up to a straight line, or 180 degrees. It's all about balance in the parallelogram family!
Common Questions
What are the angle properties of a parallelogram?
Opposite angles are equal. Consecutive (adjacent) angles are supplementary, adding up to 180 degrees. All four interior angles sum to 360 degrees.
If one angle of a parallelogram is 65 degrees, what are the others?
The opposite angle is also 65 degrees. The two adjacent angles each measure 180 - 65 = 115 degrees. Check: 65 + 115 + 65 + 115 = 360 degrees.
Why do consecutive angles of a parallelogram add to 180 degrees?
Because parallel lines cut by a transversal create co-interior (same-side interior) angles that are supplementary. The sides of a parallelogram create exactly this configuration.
What grade learns about angles of a parallelogram?
Angles of a parallelogram are a 7th grade geometry topic in Saxon Math Course 2, building on vertical and supplementary angles to analyze quadrilateral properties.
Do these angle rules apply to all parallelograms?
Yes, the rules apply to all parallelograms: rectangles, rhombuses, and squares are special parallelograms, though rectangles and squares have all 90-degree angles.
How do the angles of a parallelogram differ from a trapezoid?
A parallelogram has two pairs of parallel sides, so both pairs of opposite angles are equal. A trapezoid has only one pair of parallel sides, so only co-interior angles along the parallel sides are supplementary.