Question

5. In the figure, O is the centre of the circle. What is the measure of ∠AOC?

(i) 120°
(ii) 136°
(iii) 128°
(iv) 158°

Answer 1

5. In the figure, O is the centre of the circle.

Construction: Join OD.

In Δ AOD,

AO = OD   (radii)

∠ DAO = ∠ ADO = 48°

In Δ COD,

CO = OD   (radii)

∠ OCD = ∠ ODC = 31°

From figure, it's clear that,

∠ ADO + ∠ ODC  = ∠ ADC

48° + 31° = ∠ ADC

∠ ADC = 79°

∠ AOC = 2 × ∠ ADC

= 2 × 79°

= 158°

∴ ∠ AOC = 158°

Option (iv) is correct.

Answer 2

Answer:

AOC = 158

Step-by-step explanation:

because, dac + dca= 180

48+31=79

so, according to the theoram 10.8 the angle substended by an arc at the centre of the circle is doubled the angle substended by it at any point on the remaining part of the circle

now 79×2 is 158