A, B and C are points on the circumference of a circle, centre O.
DAE is the tangent to the circle at A.
Angle BAE = 53°
Angle CBO = 32°
Work out the size of angle CAO.
Your final line should say, CAO

CAO = 21°

Step-by-step explanation:

In a circle, the angle of tangency and the inscribed angle subtended by the same arc are equal in measures

In circle O

∵ DAE is a tangent to circle O at point A

∵ AB is a chord

∴ ∠BAE is an angle of tangency subtended by the arc AB

∵ ∠BCA is an inscribed angle subtended by the arc AB

→ By using the rule above

∴ m∠BAE = m∠BCA

∵ m∠BAE = 53°

∴ m∠BCA = 53°

In ΔBOC

∵ OB and OC are radii

∴ OB = OC

∴ ΔBOC is an isosceles Δ

→ That means its base angles are equal

∴ m∠OBC = m∠OCB

∵ m∠OBC = 32°

∴ m∠OCB = 32°

∵ m∠BCA = m∠BCO + m∠OCA

∴ 53 = 32 + m∠OCA

→ Subtract 32 from both sides

∴ 21 = m∠OCA

∴ m∠OCA = 21°

In ΔAOC

∵ OA and OC are radii

∴ OA = OC

∴ ΔAOC is an isosceles Δ

→ That means its base angles are equal

∴ m∠CAO = m∠OCA

∵ m∠OCA = 21°

∴ m∠CAO = 21°

∴ CAO = 21°

47.28 or 47.2857143

step-by-step explanation:

you just divide 331 by 7 and you get that answer. ( i think so tho)

the first option i believe

step-by-step explanation: