Question

prove that if the arms of an angle are respectively perpendicular to the arms of another angle, then the angles are either equal or supplementry​

Answer 1

$\large\bf{\underline\orange{Answer \:↝}}$

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: 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.

Answer 2

I HOPE IT'S HELPFUL FOR YOU PLEASE

THANKS MY ANSWER PLEASE