Question

In a quadrilateral ABCD, the angles A, B, C and D are in the ratio 1:2:4:5. Find the measure of each angle of the quadrilateral.

Answer 1

Sum of angles of a quadrilateral ABCD =${360}^{\circ }$

Ratio in angles = 1:2:4:5

Let first angle = x

Second angle = 2x

Third angle = 4x

and fourth angle = 5x

$\therefore$ x +2x+4x+5x = ${360}^{\circ }$

$\Rightarrow 12x={360}^{\circ }\Rightarrow x=\frac{{360}^{\circ }}{12}={30}^{\circ }$

$\therefore Firstangle={30}^{\circ }Secondangle={30}^{\circ }\times 2={60}^{\circ }Thirdangle={30}^{\circ }\times 4={120}^{\circ }Fourthangle={30}^{\circ }\times 5={150}^{\circ }$