Geometry and measuresGCSE / IGCSE

Vertically opposite angles with algebra

Solve an equation by equating vertically opposite angles.

  • Set the two opposite angle expressions equal.
  • Solve the equation, then check that both expressions give the same angle.

Example 1

Find the value of .

Vertically opposite angles are equal.Apply this to both sides.
Vertically opposite angles are equal.
Apply this to both sides.

Example 2

Find the value of .

Vertically opposite angles are equal.Apply this to both sides.
Vertically opposite angles are equal.
Apply this to both sides.

Your turn

Question 1

Find the value of .

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

Find the value of .

Check answer
Vertically opposite angles are equal.Apply this to both sides.
Vertically opposite angles are equal.
Apply this to both sides.
Question 3

Find the value of .

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

Find the value of .

Check answer
Vertically opposite angles are equal.Apply this to both sides.
Vertically opposite angles are equal.
Apply this to both sides.
Question 5

Find the value of .

Check answer
Vertically opposite angles are equal.Apply this to both sides.
Vertically opposite angles are equal.
Apply this to both sides.
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