If one side of a parallelogram is 24° less than twice the smallest angle, then the measure of the largest angle of the parallelogram is

Question

If one side of a parallelogram is 24&#xB0; less than twice the smallest angle, then the measure of the largest angle of the parallelogram is

Philoid · Accepted Answer

Let angles of parallelogram are ∠A, ∠B, ∠C, ∠D

Let smallest angle = ∠A

Let largest angle = ∠B

= ∠B = 2∠A – 24°............(i)

∠A+∠B = 180° [adjacent angle of parallelogram]

So, ∠A+2∠A -24° = 180°

= 3∠A = 180°+24° = 204°

=∠A =

= ∠B = 2×68°-24° = 112°