If an angle of a parallelogram is two-third of its adjacent angle, find the angles of the parallelogram.
Let in a parallelogram ABCD,
∠A=x
Then its adjacent angle , ∠B=23x
But, ∠A+∠B=180∘ [Since, sum of the consecutive angles of a parallelogram is 180∘.
⇒x+23x=180∘
⇒3x+2x3=180∘
⇒5x3=180∘
⇒x=180∘×35
⇒x=36∘×3
⇒x=108∘
⇒∠A=108∘---(1)
⇒∠B=180∘−108∘=72∘---(2)
Since, opposite angles of a parallelogram are equal.
⇒∠A=∠C=108∘ ---(3)
and ⇒∠B=∠D=72∘---(4)
Hence angles are 108∘,72∘,108∘,72∘.