Geometry and measuresKey Stage 3

Angles in parallelograms and rhombuses with algebra

Choose an angle equation, then solve for .

  • Equate opposite angle expressions.
  • Set adjacent angle expressions to add to .
  • These angle rules apply to both parallelograms and rhombuses.

Example 1

Find in the parallelogram.

Opposite angles are equal.Apply this to both sides.
Opposite angles are equal.
Apply this to both sides.

Example 2

Find in the rhombus.

Adjacent angles add to 180°.Apply this to both sides.Apply this to both sides.
Adjacent angles add to 180°.
Apply this to both sides.Apply this to both sides.

Your turn

Question 1

Find in the parallelogram.

Check answer
Opposite angles are equal.Apply this to both sides.
Opposite angles are equal.
Apply this to both sides.
Question 2

Find in the rhombus.

Check answer
Adjacent angles add to 180°.Apply this to both sides.Apply this to both sides.
Adjacent angles add to 180°.
Apply this to both sides.Apply this to both sides.
Question 3

Find in the parallelogram.

Check answer
Opposite angles are equal.Apply this to both sides.
Opposite angles are equal.
Apply this to both sides.
Question 4

Find in the rhombus.

Check answer
Adjacent angles add to 180°.Apply this to both sides.Apply this to both sides.
Adjacent angles add to 180°.
Apply this to both sides.Apply this to both sides.
Question 5

Find in the parallelogram.

Check answer
Opposite angles are equal.Apply this to both sides.
Opposite angles are equal.
Apply this to both sides.
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