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Parallelogram Angles Worksheet

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Parallelogram Angles Worksheet

Use the angle facts for parallelograms to solve each challenge. Opposite angles are equal, and neighbouring angles add to 180°. A rhombus has these same angle facts. Show your working where you can.

Canteen design challenge

Zach and Evie are checking parallelogram-shaped tiles for a canteen display. Find each missing angle. Diagrams are not drawn to scale.

1.A parallelogram tile has one angle of 68°. What are the sizes of the other three angles?

2.One angle in a parallelogram is 117°. Find the angle opposite it and both neighbouring angles.

3.A parallelogram has neighbouring angles labelled x and 4x. Work out x and both angle sizes.

4.True or false: If one angle in a parallelogram is 90°, all four angles are 90°. Explain using the angle facts.

Rhombus tile puzzle

Hamish notices that a rhombus is also a parallelogram. Use the same angle relationships to solve these puzzles.

5.A rhombus has one angle of 52°. Find the other three angles.

6.In a rhombus, one angle is 134°. What is the size of each of the other three angles?

7.In parallelogram ABCD, angle ABC = 73°. Find angle BCD, angle CDA and angle DAB.

8.In rhombus PQRS, angle QPS = 120°. Find angle PQR, angle QRS and angle RSP.

9.Zach says a parallelogram with one angle of 85° has a neighbouring angle of 85° too. Is he correct? Give the correct neighbouring angle and explain.

10.A parallelogram has neighbouring angles (2x + 10)° and (x + 20)°. Find x, then find both angles.

11.Create a parallelogram with one angle of 40°. Draw it and label all four angles. What angle pattern must your drawing show?