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Question

In the given construction of a ΔABC, CAB will be


A
55
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B
45
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C
75
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D
60
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Solution

The correct option is B 45


In ΔAXB
PQ is the perpendicular bisector of XA, the two triangles formed are congruent by SAS rule.
AB = XB
BAX=AXB

ABC=BAX+AXB
= 2 AXB=LXY
[Since AXB is angle bisector of LXY]

Similarly, ACB=MYXTherefore, ABC=75 and BCA=60In ΔABC, we haveABC+BCA+CAB=18075+60+CAB=180CAB=180135CAB=45


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