Adding adjacent instead of opposite angles in cyclic quadrilateral H
"The Adjacent Angle Error"
The Mistake in Action
ABCD is a cyclic quadrilateral. Angle A = 75°. Find angle B.
Wrong: Angle B = 180° - 75° = 105°
Why It Happens
Students correctly remember that angles add to 180° but apply this to adjacent angles instead of opposite angles.
The Fix
In a cyclic quadrilateral, OPPOSITE angles sum to 180°.
A is opposite to C, and B is opposite to D.
If angle A = 75°:
- Angle C = 180° - 75° = 105° ✓
- Angle B cannot be found from angle A alone (they're adjacent, not opposite)
Memory aid: Draw diagonal lines connecting opposite corners to remind yourself which pairs add to 180°.
Spot the Mistake
Can you identify where this student went wrong?
ABCD cyclic quad, angle A = 75°
Angle B = 180° - 75° = 105°
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: