Question

Quadrilateral ABCD is inscribed in a circle. Find the measure of each of the angles of the quadrilateral. Show

your work.

Answer 1

• A= 94°, B = 102°, C = 86°, D = 78°

Explanation:

ABCD is a cyclic quadrilateral

It has the property that opposite angles are supplementary: A with C and B with D.

Solve following for x:

• x + 6 + x - 2 = 180°
• 2x + 4 = 180°
• 2x = 176°
• x = 88°

The angles are:

• A = 88° + 6° = 94°
• C = 180° - 94° = 86°
• D = 88° - 10° = 78°
• B = 180° - 78° = 102°