Find the measure of each angle of a parallelogram, one its angle is 30 less than twice the smaller angle.
Let measure of smaller angle A be x, then measure of major angle B be (2x−30)⇒ ∠A+∠B=180o [ Sum of adjacent angles in parallelogram is supplementary ]
⇒ x+(2x−30)=180o
⇒ 3x−30=180o
⇒ 3x=210o
⇒ x=70o
⇒ ∠A=x=70o
⇒ ∠B=(2x−30)o=(2×70−30)o=110o
We know that opposite angles are equal in parallelogram
∴ ∠A=∠C=70o
∴ ∠B=∠D=110o