Question

Abcd is a cyclic quadrilateral. o is the center of the circle ∠bad = 40°,then angle BCD=?,m(arc BCD) =?,m( arc BAD)=?

Answer 1

Answer:

m∠BCD = 140°

m(arc BCD) = 80°

m(arc BAD) = 280°

Step-by-step explanation:

1. In the cyclic quadrilateral, every two opposite angles are supplementary.
2. 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°.