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 180180^\circ).

Given:

  • One angle = 6060^\circ
  1. Opposite angle: In a parallelogram, opposite angles are equal, so the opposite angle is also 6060^\circ.

  2. Adjacent angle: Adjacent angles in a parallelogram are supplementary, meaning their sum is 180180^\circ. Therefore, the adjacent angle is: 18060=120180^\circ - 60^\circ = 120^\circ

Thus, the opposite angle is 6060^\circ and the adjacent angle is 120120^\circ.

Would you like more details or have any questions?

Here are some related questions:

  1. What is the sum of the interior angles of a parallelogram?
  2. How do we prove that adjacent angles of a parallelogram are supplementary?
  3. Can a parallelogram have all angles equal? What type of parallelogram would that be?
  4. What other properties of a parallelogram can be derived from its angles?
  5. How would the problem change if one angle was 9090^\circ?

Tip: In any quadrilateral, the sum of all interior angles is always 360360^\circ.

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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