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

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.

Solution:

Let $x$ be the measure of each angle.

Then the ratio becomes $x: 2 x: 4 x: 5 x$.

Since, the sum of all angles in a quadrilateral is $360^{\circ}$, we have:

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

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

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

$\Rightarrow x=30^{\circ}$

Thus, the angles are :

$x=30^{\circ}$

$2 x=60^{\circ}$

$4 x=120^{\circ}$

$5 x=150^{\circ}$

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