Question

Lines and Angles / 133
the figure, two lines AB and CD intersect at point O. OP and OQ are bisectors of
AOC respectively. Show that POQ is a straight line.
4. In the figure, two lix
BOD and ZAOC resper
(2015-J8ANTMO)​

Answer 1

Answer:

∠PQ = 180° => PQ is a straight line

Step-by-step explanation:

wo lines AB and CD intersect at point O. OP and OQ are bisectors of

AOC & BOD respectively. Show that POQ is a straight line.

Let say ∠ AOC = 2x   Then ∠BOD = 2x  ( opposite angles are equal)

∠ AOC + ∠ AOD = 180°  ( straight Line)

=>  ∠ AOD = 180° -  ∠ AOC

=>  ∠ AOD = 180° -  2x

OP is bisector of ∠AOC   then ∠AOP = 2x/2 = x

OQ is bisector of ∠BOD  Then ∠DOQ = 2x/2 = x

∠PQ = ∠AOP + ∠AOD + ∠DOQ

=> ∠PQ = x + 180° -  2x + x

=> ∠PQ = 180°

=> PQ is a straight line