Math Problem Statement
One angle of a parallelogram is 60°. Find its opposite angle and the adjacent angle.
Solution
In a parallelogram, opposite angles are equal, and adjacent angles are supplementary (i.e., their sum is ).
Given:
- One angle =
-
Opposite angle: In a parallelogram, opposite angles are equal, so the opposite angle is also .
-
Adjacent angle: Adjacent angles in a parallelogram are supplementary, meaning their sum is . Therefore, the adjacent angle is:
Thus, the opposite angle is and the adjacent angle is .
Would you like more details or have any questions?
Here are some related questions:
- What is the sum of the interior angles of a parallelogram?
- How do we prove that adjacent angles of a parallelogram are supplementary?
- Can a parallelogram have all angles equal? What type of parallelogram would that be?
- What other properties of a parallelogram can be derived from its angles?
- How would the problem change if one angle was ?
Tip: In any quadrilateral, the sum of all interior angles is always .
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Math Problem Analysis
Mathematical Concepts
Geometry
Angles in Parallelograms
Supplementary Angles
Formulas
Opposite angles in a parallelogram are equal
Adjacent angles in a parallelogram are supplementary (sum to 180°)
Theorems
Parallelogram angle theorem
Suitable Grade Level
Grades 6-8