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Question

In the given construction,

  • PQ is the perpendicular bisector AX
  • RS is the perpendicular bisector AY
  • XA is the angle bisector of the LXY
  • YA is the angle bisector of the MYX

Then find the value of CAB.


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Solution

From construction
AB = XB (Since B is a point on the perpendicular bisector of AX)
BAX=AXB (angles opposite to equal sides are equal)

ABC=BAX+AXB=2AXB=LXY

( XA is the bisector of the LXY )

Therefore, ABC=75

Similarly, ACB=MYX
Therefore, BCA=60

In ABC, we have,
ABC+BCA+CAB=180
75+60+CAB=180
Then CAB=180135
Therefore CAB=45

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