In figure, if AOB is a line, OP bisects ∠BOC and OQ bisects ∠AOC, show that ∠POQ is a right angle.

Solution

∠POQ = ∠POC + ∠COQ

equals 1 half angle BOC plus 1 half angle AOC space space space space space space space space space space space space space left enclose table row cell because space OP space bisects space angle AOC end cell row cell therefore space angle POC equals 1 half angle BOC end cell row cell because space OQ space bisects space angle AOC end cell row cell therefore angle COQ equals 1 half angle AOC end cell end table end enclose equals 1 half left parenthesis angle BOC plus angle AOC right parenthesis equals space 1 half left parenthesis 180 degree right parenthesis space space space space space vertical line space L i n e a r space P a i r space A x i o m equals space 90 degree space space space space space space space space

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