One angle of a parallelogram is 60°. Find its opposite angle and the adjacent angle.

In a parallelogram, opposite angles are equal, and adjacent angles are supplementary (i.e., their sum is \(180^\circ\)).

Given:
- One angle = \(60^\circ\)

1. **Opposite angle**: In a parallelogram, opposite angles are equal, so the opposite angle is also \(60^\circ\).

2. **Adjacent angle**: Adjacent angles in a parallelogram are supplementary, meaning their sum is \(180^\circ\). Therefore, the adjacent angle is:
   \[
   180^\circ - 60^\circ = 120^\circ
   \]

Thus, the opposite angle is \(60^\circ\) and the adjacent angle is \(120^\circ\).

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 \(90^\circ\)?

**Tip**: In any quadrilateral, the sum of all interior angles is always \(360^\circ\).

Learn how to find the opposite and adjacent angles in a parallelogram when one angle is 60°. This geometry problem explores the properties of parallelograms, including the supplementary nature of adjacent angles and the equality of opposite angles. Ideal for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation