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Parallelogram and Rhombus Angles

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Parallelogram and Rhombus Angles

Use the angle facts and diagrams to solve each challenge. Show working where asked. Angles are measured in degrees (°).

Angle toolkit

In a parallelogram, opposite angles are equal and neighbouring angles add to 180°. A rhombus has these same angle properties. Its diagonals also bisect the vertex angles.

1.A designer is checking a parallelogram-shaped shade sail. One interior angle is 68°. What are the other three interior angles?
2.A rhombus paving tile has one angle of 124°. Choose the correct set of its four interior angles.
  • 124°, 56°, 124°, 56°
  • 124°, 124°, 124°, 124°
  • 124°, 56°, 56°, 56°
  • 124°, 66°, 124°, 66°
3.True or false: In every parallelogram, each pair of neighbouring interior angles adds to 180°.
TrueFalse
4.In parallelogram ABCD, angle DAB is 73°. Find angle ABC, the neighbouring angle.
5.A rhombus has one angle of 90°. What must all four interior angles be?
6.In rhombus PQRS, angle PQR is 96°. Find angles QRS, RSP and SPQ.

Crack the missing-angle codes

Let x stand for the missing angle. Use opposite-angle equality or the 180° neighbouring-angle rule, then solve.

7.In a parallelogram, neighbouring angles are (3x + 5)° and (2x + 25)°. Find x and both angle measures.
8.One angle of a rhombus is (4x − 10)°. Its neighbouring angle is (2x + 10)°. Find x, then state the four angles.
9.A rhombus diagonal bisects a vertex angle. That full vertex angle is 84°. What angle does the diagonal make with either side at that vertex?
10.Explain why a parallelogram cannot have two neighbouring interior angles of 95° and 95°.

2 printable pages

  • Parallelogram and Rhombus Angles, page 1 of 2: Angle toolkit

    Page 1

  • Parallelogram and Rhombus Angles, page 2 of 2: Crack the missing-angle codes

    Page 2

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