Question

Adjacent angles of a parallelogram are in the ratio of $1:2$, find the measures of the smallest angles of the parallelogram

Answer 1

The ratio of adjacent angles of a parallelogram are $1:2$

$\Rightarrow$ Let the adjacent angles are $x$ and $2x$

We know, that sum of the adjacent angles of parallelogram is ${180}^o$

$\therefore$ $x+2x={180}^o$

$\Rightarrow$ $3x={180}^o$

$\Rightarrow$ $x={60}^o$

Adjacent angles are,

$\Rightarrow$ $x={60}^o$

$\Rightarrow$ $2x=2\times {60}^o={120}^o$

$\therefore$ The smallest angle is ${60}^o$