Question

In the given figure, O is the centre of the circle. If
ZOAB = 52° and AB = BC find the measure of
ZAOC
Please Answer Fast
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Answer 1

Answer:

<AOC = 152°

Step-by-step explanation:

OA=OB=OC ( radius of circle)

In ∆AOB and ∆BOC

OA = OC (radius of circle)

OB = OB (common)

AB = BC (Given)

so ∆AOB is congurant to ∆BOC by SSS rule.

so <AOB = <BOC. .......(I)

In,∆AOB

OA=OB

<OAB = <OBA. (angles opposite to equal sides are equal)

<AOB + <OAB + <OBA=180 (Angle sum property)

<AOB = 180°-52°-52°

<AOB = 76° .......(ii)

from (I) and (ii)

<AOC = <AOC +<BOC

= 76°+76°

= 152°