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 xx and yy step by step:

(a) Work out the size of the angle marked xx:

  1. Property of a parallelogram: Opposite angles are equal, and adjacent angles are supplementary (sum to 180180^\circ).
  2. The angle 6464^\circ is adjacent to xx. Thus, x+64=180x + 64^\circ = 180^\circ.
  3. Solving for xx: x=18064=116x = 180^\circ - 64^\circ = 116^\circ

So, the size of angle xx is: x=116x = 116^\circ


(b) Work out the size of the angle marked yy:

  1. Opposite angles are equal: The angle yy is opposite to the given 6464^\circ.
  2. Therefore, y=64y = 64^\circ.

Final Answers:

  • (a) x=116x = 116^\circ
  • (b) y=64y = 64^\circ

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:

  1. What is the sum of all interior angles in a parallelogram?
  2. How can you prove that adjacent angles in a parallelogram are supplementary?
  3. If one angle of a parallelogram is a right angle, what does that imply about the shape?
  4. How does the property of opposite angles help in solving real-world problems involving parallelograms?
  5. 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