Geometry and measuresKey Stage 3

Angles in a kite with algebra

Solve first, then use all four interior angles to solve .

  • Set the equal opposite angles equal to find .
  • Substitute to find the actual angles.
  • Use the quadrilateral total to find the last angle, then solve for .

Example 1

Find in the kite.

The opposite angles between the unequal sides are equal.Apply this to both sides.
The opposite angles between the unequal sides are equal.
Apply this to both sides.

Example 2

Find and in the kite.

The opposite angles between the unequal sides are equal.Apply this to both sides.
Substitute into either side-angle expression.
Each equal angle
The four interior angles add to 360°.Apply this to both sides.Apply this to both sides.
The opposite angles between the unequal sides are equal.Apply this to both sides.
Substitute into either side-angle expression.
Each equal angle
The four interior angles add to 360°.
Apply this to both sides.Apply this to both sides.

Your turn

Question 1

Find in the kite.

Check answer
The opposite angles between the unequal sides are equal.Apply this to both sides.
The opposite angles between the unequal sides are equal.
Apply this to both sides.
Question 2

Find and in the kite.

Check answer
The opposite angles between the unequal sides are equal.Apply this to both sides.
Substitute into either side-angle expression.
Each equal angle
The four interior angles add to 360°.Apply this to both sides.Apply this to both sides.
The opposite angles between the unequal sides are equal.Apply this to both sides.
Substitute into either side-angle expression.
Each equal angle
The four interior angles add to 360°.
Apply this to both sides.Apply this to both sides.
Question 3

Find in the kite.

Check answer
The opposite angles between the unequal sides are equal.Apply this to both sides.
The opposite angles between the unequal sides are equal.
Apply this to both sides.
Question 4

Find and in the kite.

Check answer
The opposite angles between the unequal sides are equal.Apply this to both sides.
Substitute into either side-angle expression.
Each equal angle
The four interior angles add to 360°.Apply this to both sides.Apply this to both sides.
The opposite angles between the unequal sides are equal.Apply this to both sides.
Substitute into either side-angle expression.
Each equal angle
The four interior angles add to 360°.
Apply this to both sides.Apply this to both sides.
Question 5

Find in the kite.

Check answer
The opposite angles between the unequal sides are equal.Apply this to both sides.
The opposite angles between the unequal sides are equal.
Apply this to both sides.
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