Angles of a quadrilateral are 4x- - 5x-2- - 7x-20- and 6x-3- What will be the value of x-

Given, The angles of a quadrilateral are (4x)^∘ , 5(x+2)^∘ , (7x 20)^∘ and 6(x+3)^∘. We know that the sum of all the interior angles in a quadrilateral is 360^∘ ...

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Standard VIII

Mathematics

Angle Sum Property of a Quadrilateral

Angles of a q...

Question

Angles of a quadrilateral are $(4 x)^{\circ}, 5 (x + 2)^{\circ}, (7 x - 20)^{\circ}$ and $6 (x + 3)^{\circ}$ . What will be the value of $x$ .

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Solution

Given,
The angles of a quadrilateral are $(4 x)^{\circ}, 5 (x + 2)^{\circ}, (7 x - 20)^{\circ}$ and $6 (x + 3)^{\circ}$ .
We know that the sum of all the interior angles in a quadrilateral is $360^{\circ}$
Hence,
$(4 x)^{\circ} + 5 (x + 2)^{\circ} + (7 x - 20)^{\circ} + 6 (x + 3)^{\circ} = 360^{\circ} 4 x + 5 x + 10^{\circ} + 7 x - 20^{\circ} + 6 x + 18^{\circ} = 360^{\circ} 22 x + 8^{\circ} = 360^{\circ} 22 x = 360^{\circ} - 8^{\circ} 22 x = 352^{\circ} x = {(\frac{352}{22})}^{\circ} we get. x = 16^{\circ}$

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Angles of a quadrilateral are (4x)∘ , 5(x+2)∘ , (7x−20)∘ and 6(x+3)∘. What will be the value of x.

Angles of a quadrilateral are $(4 x)^{\circ}, 5 (x + 2)^{\circ}, (7 x - 20)^{\circ}$ and $6 (x + 3)^{\circ}$ . What will be the value of $x$ .