Question

If the angles of a quadrilateral are x, x + 30°, x + 60 and 4x then the difference between greatest angle and the smallest is8​

Answer 1

$\underline{\underline{\sf{\maltese\:\:Given}}}$

$\sf Angles \: of \: a \: quadrilateral \: are :$

$\sf \implies First \: angle : x$

$\sf \implies Second \: angle : x + 30^ \circ$

$\sf \implies Third \: angle : x + 60^ \circ$

$\sf \implies Fourth \: angle : 4x$

$\underline{\underline{\sf{\maltese\:\:To \: find }}}$

$\sf \implies Difference \: between \: greatest \: angle \: and \: the \: smallest \: angle= \: ?$

$\underline{\underline{\sf{\maltese\:\:Solution }}}$

$\sf \dashrightarrow \underline{ \boxed{ \sf Sum \: of \: the \: interior \: angles \: of \: quadrilateral = 360 ^ \circ}}$

$\small{ \bf So, }$

$\sf \implies x + x + 30^ \circ+ x + 60^ \circ + 4x = 360 ^ \circ$

$\sf \implies 7x + 90^ \circ = 360 ^ \circ$

$\sf \implies 7x = 360 ^ \circ - 90^ \circ$

$\sf \implies 7x = 270 ^ \circ$

$\sf \implies x = \dfrac{270 ^ \circ}{7}$

$\sf \star \: \underline{ Angles \: of \: the \: quadrilateral \: are : }$

$\sf \implies First \: angle \: (x) = \dfrac{270 ^ \circ}{7}$

$\sf \implies Second \: angle \: (x + 30^ \circ) = \dfrac{270 ^ \circ}{7} + 30^ \circ = \dfrac{480 ^ \circ}{7}$

$\sf \implies Third \: angle \: (x + 60^ \circ) = \dfrac{270 ^ \circ}{7} + 60^ \circ = \dfrac{690 ^ \circ}{7}$

$\sf \implies Fourth \: angle \: ( 4x) = 4 \times \dfrac{270 ^ \circ}{7} = \dfrac{1080^ \circ}{7}$

$\small{ \bf Now, }$

$\sf \star \: Difference \: between \: greatest \: angle \: and \: the \: smallest \: angle:$

$\sf \implies Greatest \: angle = \dfrac{1080^ \circ}{7}$

$\sf \implies Smallest \: angle = \dfrac{270 ^ \circ}{7}$

$\small{ \bf So, }$

$\sf \implies \dfrac{1080^ \circ}{7} - \dfrac{270 ^ \circ}{7}$

$\sf \implies \dfrac{1080^ \circ - 270 ^ \circ}{7}$

$\sf \implies \dfrac{810 ^ \circ}{7} \: \: or \: \: 115.71^ \circ$

$\small{ \bf Therefore, }$

$\sf \implies Difference \: between \: greatest \: angle \: and \: the \: smallest \: angle= \dfrac{810^\circ}{7} \: \: or \: \: 115.71^\circ$

Answer 2

Given :   the angles of a quadrilateral are x, x + 30°, x + 60 and 4x  

To Find :  the difference between greatest angle and the smallest angle is

Solution:

angles of a quadrilateral are x, x + 30°, x + 60 and 4x

Sum of all angles of Quadrilateral = 360°

x + x + 30° + x + 60° + 4x =  360°

=> 7x = 270°

=> x = 270° / 7

Smallest x = 270° / 7   and

Largest  4x = 4*  270° / 7

Difference  = 4x - x  = 3 *  270° / 7   =  115.7°

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