Question

Three angles of the quadrilateral are in the ratio 1: 2: 3 and the sum of the smallest and the greatest
angle is 180°. Find all the angles of the quadrilateral.​

Answer 1

Step-by-step explanation:

$1x = 2x = 3x = 180 \\ \\ 6x = 180 \\ \\ x = \frac{180}{6} \\ \\ x = 30 \\ \\ 1st \: angle \: = 1x = 1 \times 30 = 30 {}^{0} \\ \\ 2nd \: angle \: = 2x = 2 \times 30 = 60 {}^{0} \\ \\ 3rd \: angle \: = 3x = 3 \times 30 = 90 {}^{0} \\ \\ 4th \: angle \: = \\ \\ sum \: of \: all \: angle \: of \: angles \: \\ of \: a \: quadriateral \: is \: 360 {}^{0} \\ \\ let \: 4th \: angle \: be \: = x \\ \\ 30 + 60 + 90 + x = 360 \\ \\ 180 + x = 360 \\ \\ x = 360 - 180 \\ \\ x = 180 {}^{0}$