Question

The angles of a quadri lateral care in the ration
3:7:1:9. Find the measure of each of its angles​

Answer 1

Let the ratio be x.

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By comparing to given figure,

• ∠ABC = 3x
• ∠BCA = 7x
• ∠CDA = 1x
• ∠DAB = 9x

∵ Sum of all angles of quadrilateral is 360.

$\bf ∠ABC + ∠BCA + ∠CDA + ∠DAB = 360 \\ \\ \bf \implies 3x + 7x + 1x + 9x = 360 \\ \\ \bf \implies \: 20x = 360 \\ \\ \bf \implies \: x = \frac{360}{20} \\ \\ \large \implies \boxed {\boxed {\tt \blue {x = 18 }}}$

∴ Angles of quadrilateral will be:

• ∠ABC = 3x = 3×18 = 54°
• ∠BCA = 7x = 7×18 = 126°
• ∠CDA = 1x = 1×18 = 18°
• ∠DAB = 9x = 9×18 = 162°

Answer 2

Given ,

The ratio of angles of quadrilateral are 3:7:1:9

Let us assume that ,

The angles of quadrilateral be 3x , 7x , x , 9x

We know that , the sum of angles of quadrilateral is 360

Thus ,

$\sf \mapsto 3x + 7x + x + 9x = 360 \\ \\\sf \mapsto 20x = 360 \\ \\\sf \mapsto x = \frac{360}{20} \\ \\ \sf \mapsto x = 18$

$\therefore \sf \underline{The \: angles \: are \: 54 , 126 , 18 , 162}$