Question

The measure of arc BCD is

80 degrees
40 degrees
100 degrees
140 degrees

please show work!!!

Answer 1

m∠BCD = 140°

Explanation:

ABCD is cyclic quadrilateral. A property of cyclic quadrilateral states that the opposite angles of it sum up to 180°. Here:

m∠A + m∠C =180° and m∠B + m∠D = 180°

So, m∠A + m∠C =180°

m∠A = 40° (given in the question)

40° + m∠C = 180°

m∠C = 180° - 40° = 140°

∴m∠C = m∠BCD = 140°