Question:
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.
Solution:
Consider be angles AOB and ACB
Given 0A perpendicular to A0, also 0B perpendicular to BO
To Prove: ∠AOB + ∠ACB = 180° (or) ∠AOB + ∠ACB = 180°
Proof: In a quadrilateral = ∠A + ∠O + ∠B + ∠C = 360°
[Sum of angles of quadrilateral is 360]
⟹ 180 + O + B + C = 360
⟹ O + C = 360 - 180
Hence AOB + ACB = 180 .... (1)
Also, B + ACB = 180
⟹ ACB = 180 - 90 = ACES = 90° .... (2)
From (i) and (ii), ACB = A0B = 90
Hence, the angles are equal as well as supplementary.