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Question

In ΔABC,AB=AC,A=40,O is a point inside ΔABC such that OBC=OCA. Find the measure of BOC.

A
110
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B
35
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C
140
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D
155
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Solution

The correct option is A 110
Given: AB = AC
ABC=ACB ...(i) {Angle opposite equal sides}
Also, OBC=OCA ...(ii) {given}
Subtract (i) from (ii)
OBA=OCB ...(iii)
Let OBC=OCA=x
and OBA=OCB=y
ABC=ACB=x+y
In ABC,
ABC+BAC+BCA=180
{Using Angle Sum Property}
40 + (x + y) + (x + y) =180
2(x+y)=140
x+y=70
In OBC,
OBC+OCB+BOC=180
x+y+BOC=180
BOC=180(x+y)
BOC=18070=110


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