Question

in the given figure angle ABC=30. find angle AOC​

Answer 1

Answer:

"60°

Step-by-step explanation:

∠AOB = 90° (given) ∵ OA = OB (Radius of circle) ∴ ∠OAB = ∠OBA = x (Let) In ΔOAB ∠OAB + ∠OBA + ∠AOB = 180° ⇒ x + x + 90° = 180° ⇒ 2x = 180° – 90° ⇒ x = 90 ∘ 2 90∘2 = 45° ∴ ∠OAB = 45° ∠OBA = 45° We know that angles subtended by arc at centre of circle double the angle subtended at remaining part of circle. ∠AOB = 2∠ACB ∠ACB = 1 2 12 ∠AOB = 1 2 12 × 90° = 45° Now, on ΔABC ∠ACB + ∠BAC + ∠CBA = 180° ∠ACB + [∠BAO + ∠CAO] + ∠CBA = 180° ⇒ 45° + (45° + ∠CAO) + 30° = 180° ⇒ ∠CAO = 180° – (30° + 45° + 45°) ⇒ ∠CAO = 180° – 120° ⇒ ∠CAO = 60°""

Answer 2

Answer:

the given figure angle ABC=30. find angle AOC