Question

If angles of a quadrilateral are in the ratio of 1:2:3:4, then the largest angle of the quadrilateral is .

• A. 150°
• B. 108°
• C. 144°
• D. 72°

Answer 1

The correct option is C 144°

Let the angles of the quadrilateral be x°, 2x°, 3x° and 4x°.

By angle sum property, the sum of interior angles of a quadrilateral is 360°.
$\Rightarrow \angle A+\angle B+\angle C+\angle D=360°$
$\Rightarrow x°+2x°+3x°+4x°=360°$
$\Rightarrow 10x°=360°$
$\Rightarrow x°=36°$

So, the angles of quadrilateral are,
x° = 36°,
2x° = 72°,
3x° = 108°,
4x° = 144°.
Hence, the largest angle of the quadrilateral is 144°.