Ans quickly Q.22. In the given figure, arc APB : arc BQC = 2 : 3 and ∠ AOC = 150 ° , Then ∠ ABC is equal to (A) 150 ° (B) 75 ° (C) 105 ° (D) 135 ° Share with your friends Share 4 Brijendra Pal answered this Hi, we should know or remember the property that arc length is in the same ratio as in angle so if arc APB: arc BQC = 2:3 then angle AOB:angle BOC = 2:3so let these angle are 2x and 3x so 2x+3x = angle AOC = 150 5x = 150 degree x = 30 degreeso angle AOB = 60 degree and angle BOC = 90 degreeand since OA = OB = radius , in triangle OAB angle OBA = angle OAB and hence using angle sum property of triangle angle OAB+angle OBA +angle AOB = 180 angle OBA = angle OAB =180-602= 60similarily in triangle OBCOB = OC = radiushence angle OBC = angle OCB =180-902= 45so angle ABC = 45+60 = 105 degree 4 View Full Answer Amirthavarshini S answered this c)105o -1