What you’ll learn
Use cyclic quadrilateral properties.
Key idea
Opposite interior angles of a cyclic quadrilateral sum to 180 degrees; they need not be equal.
Opposite cyclic angles sum to 180 degrees, not necessarily equality.
Worked example
Enter the exact value or ordered values in the format requested below.
A,B,C,D are distinct vertices in order on one circle. Angle A=100 degrees. Find opposite interior angle C in degrees.
- A and C are an opposite cyclic pair, so A+C=180 degrees.
- C=180-100=80 degrees.
Answer: 80
Quick Check
Evaluate a worked attempt at use cyclic quadrilateral properties, identify the first invalid step, and provide the correction.
Cyclic ABCD has angle A=40 degrees. Step 1 pairs A and C as opposite. Step 2 sets C=40 because opposite cyclic angles are congruent. Locate and repair the first invalid step.