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