Question

If an angle of a parallelogram is two-third of its adjacent angle, find all the four angles.

Answer 1

Let $x$ and $y$ be two adjacent angles of a parallelogram.

According to the question,

$\Rightarrow$ $x=\frac{2}{3}y$ ----- ( 1 )

We know in parallelogram, sum of adjacent angles are supplementary.

$\therefore$ $x+y={180}^o.$

$\Rightarrow$ $\frac{2}{3}y+y={180}^o$ [ From ( 1 ) ]

$\Rightarrow$ $2y+3y={540}^o$

$\Rightarrow$ $5y={540}^o$

$\Rightarrow$ $y={108}^o.$

Substituting value of $y$ in equation ( 1 ) we get,

$\Rightarrow$ $x=\frac{2}{3}\times {108}^o$

$\Rightarrow$ $x={72}^o$

We know that, in parallelogram opposite angles are equal.

$\therefore$ Four angles of parallelogram are ${108}^o,{72}^o,{108}^o$ and ${72}^o.$