Question

The angles of a quadrilateral are in the ratio $3:2:4:1$. Find the angles of the quadrilateral

• A. ${108}^{\circ },{72}^{\circ },{144}^{\circ }$ and ${36}^{\circ }$.
• B. ${108}^{\circ },{62}^{\circ },{144}^{\circ }$ and ${36}^{\circ }$.
• C. ${98}^{\circ },{72}^{\circ },{144}^{\circ }$ and ${36}^{\circ }$.
• D. none of the above

Answer 1

Answer: (A)

${108}^{\circ },{72}^{\circ },{144}^{\circ }$ and ${36}^{\circ }$.

Given: The angles of a quadrilateral are in the ratio $3:2:4:1$.

We know that sum of all angles of a quadrilateral$={360}^o$

So angles of the quadrilateral are:

$\angle A=\frac{3}{10}\times {360}^o={108}^o$, $\angle B=\frac{2}{10}\times {360}^o={72}^o,\angle C=\frac{4}{10}\times {360}^o={144}^o$, $\angle D=\frac{1}{10}\times {360}^o={36}^o$

From the figure, $\angle A+\angle D={108}^o+{72}^o\Rightarrow \angle A+\angle D={180}^o$

i.e. Sum of interior angles on the same side of the transversal AB$={180}^o$.

$\therefore BC\parallel AD.$

Hence the quadrilateral is a trapezium.