Question

The four angles of a quadrilateral are in the ratio 2:3:6:7. What is the measures of each angle?

• A. 40°, 70°, 120°, 130°
• B. 40°, 60°, 120°, 140°
• C. 40°, 60°, 110°, 150°
• D. 50°, 50°, 120°, 140°

Answer 1

The correct option is B 40°, 60°, 120°, 140°

Given,
The ratio of angles of a quadrilateral is 2:3:6:7.

We know that the sum of all the interior angles of a quadrilateral is 360°.
Let the common multiple of angles be $x$
$\therefore 2x+3x+6x+7x=360°$
$\Rightarrow 18x=360°$
$\Rightarrow x=\frac{360°}{18}=20°$

So, the angles are:
$2\times 20°=40°$
$3\times 20°=60°$
$6\times 20°=120°$
$7\times 20°=140°$