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Question

In ABC, bisectors of A and B intersect at point O. If C=70. Find measure of AOB.

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Solution

Given C=70
OAB=12CAB ……(i) (AO is the bisector of CAB)
OBA=12 CBA ……(ii) (BO is the bisector of CBA)
In ABC
CAB+CBA+C=180 (Angle sum property of triangle)
CAB+CBA+70=180
CAB+CBA=18070
CAB+CBA=110
Multiply both sides by 12
12CAB+12CBA=55
OAB+OBA=55 …(iii) (From (i) and (ii))
In AOB
AOB+OAB+OBA=180 (Angle sum property of triangle)
AOB+55=180 (From (iii))
AOB=18055=125
Hence measure of AOB is 125.

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