Question

prove prove that the bisector of the angle of a linear pair are at right angle

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Answer 1

Step-by-step explanation:

the linear pair has 180° and bisector divides it into 2eq. pair

180=2x

180/2=X

X=90°

thats how the bisector of the angle of a linear pair are at right angle.

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Answer 2

☯GIVEN☯

$\angle AOC and \: \angle BOC form \: a \: linear \\ pair \: of \: angles ,OD \: and \: OE \: are \\ bisectors \: of \: \angle AOC and \: \angle BOC \\ respectivly.$

☯PROVE☯

$\angle DOE=90°$

☯SOLUTION☯

since, we know that the sum of pair of linear eq. is 180° we, have

$\angle AOC + \angle BOC = 180 \degree$

$= > \frac{1}{2} \angle AOC + \frac{1}{2} \angle BOC = \frac{1}{2} \times 180 \degree$

$= > \frac{1}{2} \angle AOC + \frac{1}{2} \angle BOC = \frac{1}{ \cancel2} \times \cancel{ 180} \degree$

$= > \angle DOC + \angle COE = 90 \degree$

$\big (∵ \angle DOC = \frac{1}{2} \angle AOC \: and \: \angle COE = \frac{1}{2} \angle BOC \big )$

$= > \angle DOE = 90 \degree$

Therefore, the bisectors of the angles of linear pair are at right angles