Question

In fig AB and CD are straight lines and op and oq are respectively the bisectors of angle bod and angle aoc.Show that the rays op and oq are in the same line

Expert pls answer this question quickly it's very urgent the answer must be correct

Answer 1

In order to prove that OP and OQ are in the same line, it is sufficient to prove that,

Angle POQ= 180°

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Answer 2

Answer:

In order to prove that OP and OQ are in the same line , it is sufficient to prove that $\angle$POQ = 180°.

Now, OP is the bisectors of $\angle$BOD

$\implies$ $\angle$1 = $\angle$6 .............. (1)

And, OQ is the bisectors of $\angle$AOC

$\therefore$ $\angle$3 = $\angle$4 ................ (2)

Clearly, $\angle$2 and $\angle$5 are vertically opposite angles

$\therefore$ $\angle$2 = $\angle$5 ................ (3)

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We know that the sum of angles formed at a point is 360°.

$\therefore$ $\angle$1 + $\angle$2 + $\angle$3 + $\angle$4 + $\angle$5 + $\angle$6 = 360°

$\implies$ ($\angle$1 + $\angle$6) + ($\angle$3 + $\angle$4) + ($\angle$2 + $\angle$5) = 360°

$\implies$ 2$\angle$1 + 2$\angle$3 + 2$\angle$2 = 360°

$\implies$ 2 ($\angle$1 + $\angle$3 + $\angle$2) = 360°

$\imples$ $\angle$1 + $\angle$3 + $\angle$2 = 180°

$\implies$ $\angle$POQ = 180°

Hence, OP and OQ are in the same line.