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 the small angle be = x

Then the second angle = 2x - 24°

Since,

Opposite angles are equal the 4 angles will be x, 2x - 24° , x , 2x - 24°

So now by angle sum property:

x + 2x - 24° + x + 2x - 24° = 360°

6x - 48° = 360°

6x = 360° + 48°

6x = 408°

x =

x = 68°

Thus, the smallest angle is 68°

The second angle = 2 (68°) - 24°

= 112°