Math Problem Statement
The diagram above shows a parallelogram. Work out the size of the angle marked x. Work out the size of the angle marked y.
Solution
The diagram represents a parallelogram. Let’s solve for the angles and step by step:
(a) Work out the size of the angle marked :
- Property of a parallelogram: Opposite angles are equal, and adjacent angles are supplementary (sum to ).
- The angle is adjacent to . Thus, .
- Solving for :
So, the size of angle is:
(b) Work out the size of the angle marked :
- Opposite angles are equal: The angle is opposite to the given .
- Therefore, .
Final Answers:
- (a)
- (b)
Would you like me to elaborate further or verify another part of the problem? Let me know!
Here are five related questions to expand your understanding:
- What is the sum of all interior angles in a parallelogram?
- How can you prove that adjacent angles in a parallelogram are supplementary?
- If one angle of a parallelogram is a right angle, what does that imply about the shape?
- How does the property of opposite angles help in solving real-world problems involving parallelograms?
- Can you apply these angle properties to non-parallelogram quadrilaterals?
Tip: Always remember, in parallelograms, adjacent angles are supplementary, and opposite angles are equal—use these properties effectively in solving problems!
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Math Problem Analysis
Mathematical Concepts
Geometry
Properties of Parallelograms
Formulas
Adjacent angles in a parallelogram are supplementary (x + adjacent = 180°)
Opposite angles in a parallelogram are equal
Theorems
Parallelogram Angle Properties
Suitable Grade Level
Grades 7-9