Question

In the figure, O is the centre of the circle and angle AOB =90°, angle ABC=30°,Then find angle CAB​

Answer 1

angke CAB=60°

Answer:

∠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∘290∘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

∠AOB = 1/2 × 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°