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.

Answer 1

Let the angles be ∠ACB and ∠ABD 

Let AC perpendicular to AB, and CD is perpendicular to BD. 

To Prove : ∠ACD = ∠ABD OR ∠ACD + ∠ABD =180° 

Proof : 

In a quadrilateral, 

∠A+ ∠C+ ∠D+ ∠B = 360° [ Sum of angles of quadrilateral is 360° ] 

180° + ∠C + ∠B = 360° 

∠C + ∠B = 360° – 180° 

Therefore, ∠ACD + ∠ABD = 180° 

And ∠ABD = ∠ACD = 90° 

Hence, angles are equal as well as supplementary.