Question -
Answer -
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 ofquadrilateral 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.