In △ ABC is incribed in a circle with center O, such that ∠ACB = 115°. O is joined to A. What is the measures of ∠OAB?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 25°
Given :
∠ACB = 115°
Calculations :
The angle subtended by an arc at the centre is double the angle subtended by the arc at any point on the circle.
⇒ ∠AOB (external) = 2 ∠ACB
⇒ ∠AOB (external) = 2(115) = 230
⇒ ∠AOB (internal) = 360 - 230 = 130
In 𐤃 ABO, AO = BO (radii)
⇒ ∠ABO = ∠BAO
⇒ ∠BAO + ∠ABO + ∠AOB = 180
⇒ ∠BAO = 1/2 × (180 - 130)
⇒ 50/2 = 25°
Hence, the value of ∠OAB = 25°.