the angles of a quadrilateral are in the ratio 1:2:3:4 find measure of the largest angle
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the angles of a quadrilateral are in the ratio 1:2:3:4 find measure of the largest angle
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Given :- The angles of a quadrilateral are in the ratio 1:2:3:4 find measure of the largest angle ?
Answer :-
Let us assume that, the angles of a quadrilateral are x , 2x , 3x and 4x respectively .
so,
sum of all angles of quadrilateral = 360° { By angle sum property.}
then,
→ x + 2x 3x + 4x = 360°
→ 10x = 360°
→ x = 36°
therefore,
→ Largest angle = 4x = 4 * 36° = 144° (Ans.)
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Given :-
To Find :-
Formula Used :-
[tex] \bigstar \: \boxed{ \bf Sum \: of \: all \: angles_{(Quadrilateral)} \: = \: 360°} \: \bigstar[/tex]
Solution :-
Given that,
[tex]⇝\;[/tex]The angles of a quadrilateral are in the ratio 1:2:3:4
Let,
[tex]⟶\;[/tex]The angles will be 1x, 2x, 3x and 4x
According to the question by using formula we get,
[tex]\sf \implies \: Sum \: of \: all \: angles \: = \: 360°[/tex]
[tex]\sf \implies \: 1x + 2x + 3x + 4x \: = \: 360°[/tex]
[tex]\sf \implies \: 3x + 3x + 4x \: = \: 360°[/tex]
[tex]\sf \implies \: 6x + 4x \: = \: 360°[/tex]
[tex]\sf \implies \: 10x \: = \: 360°[/tex]
[tex] \displaystyle\sf \implies \: x \: = \: \cancel \frac{360}{10} [/tex]
[tex] \displaystyle\sf \implies \: x \: = \: \frac{36}{1}[/tex]
[tex] \displaystyle\bf \implies \: \underline{x \: = \: 36 \degree}[/tex]
Hence,
The angles of a Quadrilateral :
[tex] \sf \longmapsto \: \: 1x = 1(36) = \bf36°[/tex]
[tex] \longmapsto \: \: \sf2x = 2(36) = \bf72°[/tex]
[tex] \longmapsto \: \: \sf3x = 3(36) = \bf108°[/tex]
[tex] \longmapsto \: \: \sf4x = 4(36) = \underline{\bf144°}[/tex]
Finally,
[tex] \boxed{ \bf \therefore The \: measure \: of \: largest \: angle \: is \: 144°} \\ \\ [/tex]