Answer:
The answer is 3, 5, and 9
Answer:
m∠BCD = 140°
Step-by-step 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°
Equal angles are usually called ''alternate angles''.
The labeled angle is what's called an inscribed angle. There's a theorem (fittingly called the inscribed angle theorem) that says the measure of this angle is half the measure of the circular arc that it subtends.
In this case, the angle is subtended by an arc measuring 180°. So
(4x + 6)° = 1/2 • 180°
4x + 6 = 90
4x = 84
x = 21
