Math Problem Statement

A parallelogram has one angle that measures 10°. What are the measures of the other three angles in the parallelogram?

Solution

In a parallelogram, opposite angles are congruent, and adjacent angles are supplementary (their sum is 180°).

Given that one angle measures 10°, we can determine the other angles as follows:

  1. Opposite angle: Since opposite angles are equal in a parallelogram, the opposite angle to the 10° angle will also measure 10°.

  2. Adjacent angles: Since adjacent angles are supplementary, the sum of the adjacent angles must be 180°. Therefore, if one angle is 10°, the adjacent angle will be: 180°10°=170°180° - 10° = 170°

    So, the adjacent angle to the 10° angle will be 170°.

  3. Opposite to the 170° angle: As before, the opposite angle will also measure 170°.

Thus, the four angles in the parallelogram are:

  • Two angles measuring 10°.
  • Two angles measuring 170°.

Would you like further details or examples on parallelograms? Let me know if you have any questions!


Here are some related questions:

  1. How do you prove that opposite angles in a parallelogram are congruent?
  2. What are the properties of a rectangle and how does it differ from a parallelogram?
  3. Can a parallelogram have all its angles equal?
  4. How do you find the area of a parallelogram given its base and height?
  5. What happens if one angle of a parallelogram is 90°?

Tip: Always remember that adjacent angles in a parallelogram add up to 180°!

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Math Problem Analysis

Mathematical Concepts

Geometry
Properties of Parallelograms
Angle Relationships

Formulas

Adjacent angles in a parallelogram are supplementary (angle1 + angle2 = 180°)

Theorems

Opposite angles of a parallelogram are congruent

Suitable Grade Level

Grades 6-8