Question

Two adjacent angles of a parallelogram are in the ratio $1:5$. Find all the angles of the parallelogram.

Answer 1

Let the two angles are $x$ and $5x$.

As we know that the adjacent angles in a parallelogram are supplementary.

$\therefore x+5x=180°$

$\Rightarrow x=\frac{180°}{6}=30°$

Therefore, the two adjacent angles of a parallelogram are $30°$ and $30°\times 5=150°$.

As we know that opposite angles in a parallelogram are equal.

Hence the angles of paralellogram are $30°,150°,30°$ and $150°$ respectively.