Question

The angles of the quadrilateral are in ratio 3:5:7:9. Find the measures of each of these angles

Answer 1

Let the ratio 3:5:7:9 be 3x,5x,7x,9x. As the sum of all angles of a quadrilateral is 360,

3x+5x+7x+9x=360;
24x=360;
x=15.

Therefore the angles are:

i) 3x=3*15=45
ii)5x=5*15=75
iii)7x=7*15=105
iv)9x=9*15=135.
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Answer 2

Hello , here .....

Sol,
$let \: \: the \: angle \: be \: \: 3x, \: \: 5x, \: \:7x, \: \: 9x \\ \\as \: \: the \: sum \: of \: the \: angles \: of \: a \: quadrilateral \\ is \: \: 360 \ \\ = > \: 3x + 5x + 7x + 9x = 360 \\ or \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 24x = 360 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ = > \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = \frac{360}{24} = 15 \\ \\ = > 3x = 3 \times 15 = 45 \\ = > 5x = 5 \times 15 = 75 \\ = > 7x = 7 \times 15 = 105 \\ = > 9x = 9 \times 15 = 135 \\ \\ \\ hence \: the \: angles \: of \: the \: qudrilateral \: are \: \: 45, \: \: 75, \: \: 105 ,\: \: 135$
Answer ......

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