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:
-
Opposite angle: Since opposite angles are equal in a parallelogram, the opposite angle to the 10° angle will also measure 10°.
-
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:
So, the adjacent angle to the 10° angle will be 170°.
-
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:
- How do you prove that opposite angles in a parallelogram are congruent?
- What are the properties of a rectangle and how does it differ from a parallelogram?
- Can a parallelogram have all its angles equal?
- How do you find the area of a parallelogram given its base and height?
- What happens if one angle of a parallelogram is 90°?
Tip: Always remember that adjacent angles in a parallelogram add up to 180°!
Ask a new question for Free
By Image
Drop file here or Click Here to upload
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
Related Recommendation
Find the Other Angles of a Parallelogram Given One Angle
Understanding Angles in a Parallelogram: Are They All Equal?
Find the Adjacent Angle in a Parallelogram When One Angle is 60°
Finding Opposite and Adjacent Angles in a Parallelogram with a 60° Angle
Explanation of Supplementary Angles in Parallelogram ABCD