Question

the angles of a quadrilateral are in the ratio 1:2:3:4 find measure of the largest angle

Answer 1

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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Answer 2

Given :-

• The angles of a quadrilateral are in the ratio 1:2:3:4

To Find :-

• What is the measure of largest angle ?

Formula Used :-

$\bigstar \: \boxed{ \bf Sum \: of \: all \: angles_{(Quadrilateral)} \: = \: 360°} \: \bigstar$

Solution :-

Given that,

$⇝\;$The angles of a quadrilateral are in the ratio 1:2:3:4

Let,

$⟶\;$The angles will be 1x, 2x, 3x and 4x

According to the question by using formula we get,

$\sf \implies \: Sum \: of \: all \: angles \: = \: 360°$

$\sf \implies \: 1x + 2x + 3x + 4x \: = \: 360°$

$\sf \implies \: 3x + 3x + 4x \: = \: 360°$

$\sf \implies \: 6x + 4x \: = \: 360°$

$\sf \implies \: 10x \: = \: 360°$

$\displaystyle\sf \implies \: x \: = \: \cancel \frac{360}{10}$

$\displaystyle\sf \implies \: x \: = \: \frac{36}{1}$

$\displaystyle\bf \implies \: \underline{x \: = \: 36 \degree}$

Hence,

The angles of a Quadrilateral :

$\sf \longmapsto \: \: 1x = 1(36) = \bf36°$

$\longmapsto \: \: \sf2x = 2(36) = \bf72°$

$\longmapsto \: \: \sf3x = 3(36) = \bf108°$

$\longmapsto \: \: \sf4x = 4(36) = \underline{\bf144°}$

Finally,

$\boxed{ \bf \therefore The \: measure \: of \: largest \: angle \: is \: 144°}$