Question

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

• A. ${36}^{\circ }$, ${72}^{\circ }$, ${108}^{\circ }$ and ${144}^{\circ }$
• B. ${54}^{\circ }$, ${72}^{\circ }$, ${118}^{\circ }$ and ${124}^{\circ }$
• C. ${15}^{\circ }$, ${72}^{\circ }$, ${90}^{\circ }$ and ${150}^{\circ }$
• D. ${18}^{\circ }$, ${32}^{\circ }$, ${108}^{\circ }$ and ${164}^{\circ }$

Answer 1

The correct option is A ${36}^{\circ }$, ${72}^{\circ }$, ${108}^{\circ }$ and ${144}^{\circ }$

Let the smallest angle of the quadrilateral be $x^{\circ }.$

Then, the other three angles will be $2x^{\circ }$, $3x^{\circ }$ and $4x^{\circ }$.

Now, we know that sum of all the angles of the quadrilateral is equal to ${360}^{\circ }$.

$x^{\circ }$ + $2x^{\circ }$ + $3x^{\circ }$ + $4x^{\circ }$ = ${360}^{\circ }$

$10x^{\circ }$ = ${360}^{\circ }$

$x^{\circ }$ = ${36}^{\circ }$

Hence, all the four angles of the quadrilateral are ${36}^{\circ }$, ${72}^{\circ }$, ${108}^{\circ }$ and ${144}^{\circ }.$