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two adjacent angles are equal. is it necessary that each of these angles will be a right angle? justify your answer.

No, it is not necessary that two adjacent angles which are equal will form a right angle.
For example, ABC and BCD are two equal adjacent angles. Each equal to 44°.
ABC+BCD=44°+44°= 88°≠ 90°

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yes, because if two adjacent anles are equal then the formed linear pair should equal to 180 

so, let 1 adjacent angle be x

then 2x=180

x=90

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hey  the so formed linear pair should be 90 

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If adjacent angles are equal. That doesn't mean that they will form a linear pair

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