Answer:
m∠BCD = 140°
m(arc BCD) = 80°
m(arc BAD) = 280°
Explanation:
- In the cyclic quadrilateral, every two opposite angles are supplementary.
- The measure of the subtended arc to an inscribed angle equals twice the measure of this angle
Let us use these facts to solve the question
∵ ABCD is a cyclic quadrilateral in circle O
∵ ∠BAD and ∠BCD are opposite angles
→ By using the 1st fact above
∴ m∠BAD + m∠BCD = 180°
∵ m∠BAD = 40°
∴ 40° + m∠BCD = 180°
→ Subtract 40° from both sides
∴ 40° - 40° + m∠BCD = 180° - 40°
∴ m∠BCD = 140°
∵ Arc BCD subtended the inscribed ∠BAD
→ By using the 2nd fact above
∴ m(arc BCD) = 2(m∠BAD)
∵ m∠BAD = 40°
∴ m(arc BCD) = 2(40°)
∴ m(arc BCD) = 80°
∵ Arc BAD subtended the inscribed ∠BCD
→ By using the 2nd fact above
∴ m(arc BAD) = 2(m∠BCD)
∵ m∠BCD = 140°
∴ m(arc BAD) = 2(140°)
∴ m(arc BAD) = 280°.