Question

The angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. Find the difference between the measure of the largest angle and the smallest angle.

• A. 144°
• B. 36°
• C. 108°
• D. 72°

Answer 1

The correct option is C

108°

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

Let the angles be $x$ , 2$x$, 3$x$ and 4$x$.

The sum of angles of a quadrilateral is 360°.

Hence we have $x$ + 2$x$+ 3$x$ + 4$x$ = 360°

10$x$ = 360°

Hence, $x$ = 36°

The measure of the smallest angle = 36°

The measure of other angles are:
$2\times {36}^{\circ }={72}^{\circ }$
$3\times {36}^{\circ }={108}^{\circ }$
$4\times {36}^{\circ }={144}^{\circ }$

The measure of the largest angle = 144°

The measure of the smallest angle = 36°

Hence, the difference = 144° - 36° = 108°