Question

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

Answer 1

Step 1: Use relationship between adjacent angles to form an equation

Let the two adjacent angles be $x,y$

According to given condition,

$x=\frac{2}{3}y$ $...\left(i\right)$

The sum of adjacent angles is ${180}^{\circ }$

Therefore, $x+y={180}^{\circ }$ $...\left(ii\right)$

Step 2 : Find the value of $x$ and $y$

From $\left(i\right),\left(ii\right)$

$\frac{2}{3}y+y={180}^{\circ }$

$\Rightarrow$ $\frac{5}{3}y={180}^{\circ }$

$\Rightarrow$ $y={108}^{\circ }$

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

Step 3: Find the remaining angles of the parallelogram

The opposite angles of a parallelogram are equal.

So, angle opposite to $x$ will also be ${72}^{\circ }$,

And, similarly, angle opposite $y$ will be ${108}^{\circ }$.

Hence all the angles of the parallelogram are ${108}^{\circ },{72}^{\circ },{108}^{\circ },{72}^{\circ }$