Q. 104.0( 22 Votes )

Prove that the two arms of an angle are perpendicular to the two arms of another angle, then the angles are either equal or supplementary.

Answer :



Consider the angles,

AOB and ACB


Given that,


OA perpendicular AO and OB perpendicular BO


To prove: AOB = ACB or,


AOB + ACB = 180o


Proof: In a quadrilateral


A + O + B + C = 360o(Sum of angles of a quadrilateral)


180o + O + C = 360o


O + C = 180o


Hence, AOB + AOC = 180o (i)


Also,


B +ACB = 180o


ACB = 180o – 90o


ACB = 90o (ii)


From (i) and (ii), we get


ACB = AOB = 90o


Hence, the angles are equal as well as supplementary.

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