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

Explanation

Given OA perpendicular AC, OB perpendicular BC
To prove: `/_AOB = /_ACB` (or) `/_AOB + /_ACB = 180^@`
Proof: - In a quadrilateral⇒`/_(A+O+B+ C) = 360^@`
[Sum of angles of quadrilateral]
`180+O+C = 360`
`⇒ O+C = 360 -180 = 180^@`
Hence, `/_AOB + /_ACB = 180^@`
Also,`/_B+ /_ACB = 180^@`
Also,`/_B+/_ACB = 180^@ `
Also,`/_B+ /_ACB = 180^@`
⇒ `/_ACB = 180 - 90^@`
⇒ `/_ACB = 90^@` .....(ii)
From (i) and (ii)
`/_ACB = /_AOB = 90^@`
Hence, the angles are equal as well as supplementary