Question

If the angles of a quadrilateral are in the ratio 1:2:3:6. Then the largest angle of the quadrilateral is:

• A. 144°,108°,60°,48°
• B. 144°, 72°,36°, 108°
• C. 30°, 60°, 90°, 120°​
• D. 10°, 20°, 30°, 40°

Answer 1

The correct option is B

144°, 72°,36°, 108°

$\text{Let the smallest angle of quadrilateral be x.}\text{Then, the angles of the quadrilateral are x, 2x, 3x, 6x.}\text{Sum of the angles of a quadrilateral is}{360}^{\circ }.\to {360}^{\circ }=x+2x+3x+6x\to 12x={360}^{\circ }\to x={30}^{\circ }\therefore 2x={60}^{\circ },3x={90}^{\circ },6x={180}^{\circ }$
$\therefore \text{The largest angle of the given quadrilateral is}{180}^{\circ }$