Question

the angles of a quadrilateral are in ratio 1:2:3:4.what will be the measure of its smallest angle.

Answer 1

Step-by-step explanation:

⇒  Let the measure of angles be x,2x,3x and 4x.

We know that sum of measure of all four angles is 360o.

∴  x+2x+3x+4x=360o

⇒  10x=360o

⇒  x=36o

⇒  2x=2×36o=72o

⇒  3x=3×36o=108o

⇒  4x=4×36o=144o

⇒  The measures of angles of quadrilateral are 36o,72o,108o and 144o.

⇒ We can see measure of all 4 angles are different so, the given quadrilateral is trapezium.

Answer 2

Step-by-step explanation:

sum of angles of quadrilateral=360°

$let \: angle \: be \: x \\ 1x + 2x + 3x + 4x = 10x \\ 10x = 360 \: degree \\ x = 360 \div 10 = 36 \\ so \: smallest \: angle \: is \: x \: which \: is \: 36 \: degree$