Math Problem Statement
Solution
To solve for the measure of angle in parallelogram , we will use properties of parallelograms and the given information from the image.
Step-by-step approach:
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Properties of a parallelogram: In any parallelogram, opposite angles are equal, and adjacent angles are supplementary (they add up to ).
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Given angles:
- Angle is .
- Angle is .
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Relationship between angles and : Since and are adjacent angles in a parallelogram, they must add up to . Therefore, we can write:
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Solve for : Subtract 40 from both sides: Divide by 4:
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Find angle : Since , substitute :
Thus, the measure of angle is 105°.
Would you like more details or have any questions?
Here are 5 related questions to extend the problem:
- What is the measure of angle ?
- How do you calculate angle in parallelogram ?
- What would happen if the values of the angles were swapped?
- Can you verify if the opposite angles in parallelogram are equal?
- How would you check if the sides of parallelogram are congruent?
Tip: In any parallelogram, knowing one angle allows you to find all other angles due to symmetry and supplementary relationships!
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Math Problem Analysis
Mathematical Concepts
Geometry
Properties of Parallelograms
Algebra
Formulas
Sum of adjacent angles in a parallelogram: angle L + angle O = 180°
Expression for angle L: (x + 40)°
Expression for angle O: (3x)°
Theorems
Adjacent angles in a parallelogram are supplementary
Suitable Grade Level
Grades 8-10
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