Question

In the figure given below, if ZOAB = 400 then ZACB is
40°
A
B​

Answer 1

Step-by-step explanation:

In △OAB,

OA = OB [radii of same circle]

∠OBA = ∠OAB = 40° [∠s opp. to equal sides in a △ are equal]

Now, ∠OAB + ∠AOB + ∠OBA = 180° [angle sum properly of a △]

⇒ 40° + ∠AOB + 40° = 180°

⇒ ∠AOB = 100°

Therefore, ∠ACB = 50° [∵ angle subtended by an arc at the centre is double the angle subtended by it at the remaining part of the circle]

Answer 2

Answer

80*

Step-by-step explanation:

We know, the angle subtended by an arc of a circle at the centre is double the angle subtended by it at any point on the remaining part of the circle

Hence,In given circle,

∠POR=2∠PQR

Therefore ∠POR=2×40degree

=80degree