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find the measure of each angle of a parallelogram, if one of its angle is 30 degree less than twice of the smallest angle.

Asked by Kirti Maurya(student) , on 5/3/11

EXPERT ANSWER

Hi!
Here is the answer to your question.
 
Let ∠A be the smallest angle of the parallelogram ABCD
∠A = ∠C  (opposite angles of parallelogram are equal)
∠B = ∠D  (opposite angles of parallelogram are equal)
Given, ∠B = 2∠A – 30° 
∠A + ∠B = 180°  (sum of consecutive interior angles is supplementary)
⇒ ∠A + (2∠A – 30°) = 180°
⇒ 3∠A = 210°
⇒∠A = 70
∠B = 2 × 70° – 30° = 140° – 30° = 110°
Thus, ∠A = ∠C = 70° and ∠B = ∠D = 110° 
 
Cheers!

Posted by Lalit Mehra(MeritNation Expert)on 9/3/11

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