Question

find the measures of the four angles of a quadrilateralif they are in the ratio 3:5:7:9

Answer 1

Let angle A = 3x
B = 5x
C = 7x
D = 9x

we know that sum of all angles of quadrilateral is 360°

A+B+C+D = 360°
3x+5x+7x+9x = 360°
24x = 360°
x = 360°/24
x = 15°

So, angle A = 15°
B = 3×15 = 45°
C = 5×15 = 75°
D = 7× 15 = 105°

Answer 2

$Let \: the \: four \: angles \: of \: a \: quadrilateral \: \: be \: x \\ \\ 1st \: angles \: = 3x \\ \\ 2nd \: angles = 5x \\ \\ 3rd \: angles = 7x \\ \\ 4th \: angles = 9x \\ \\ A.T.Q. \\ \\ 3x + 5x + 7x + 9x = 360 \: \: \: (sum \: of \: a \: quadrilateral \: is \: 360 \: degree) \: \: \\ \\ 24x = 360 \\ \\ x = \frac{360}{24} \\ \\ x = 15 \\ \\ 1st \: angles \: = 3x = 3 \times 15 = 45 \: degree \\ \\ 2nd \: angles = 5x = 5 \times 15 = 75 \: degree \\ \\ 3rd \: angles = 7x = 7 \times 15 = 105 \: degree \\ \\ 4th \: angles = 9x = 9 \times 15 = 135 \: degree$