# 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. Consider the angles,

AOB and ACB

Given that,

OA perpendicular AO and OB perpendicular BO

To prove: AOB = ACB or,

AOB + ACB = 180o

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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