Question

9. If three angles of a quadrilateral are in the ratio 3:2:1 and the fourth angle is equal to these three, then find the value of smallest angle. (1) 15° (2) 20° (3) 30° (4) 40°

11th - 12th Class

Maths

Solution

457

4.0 (1 ratings)

9. (3) Let three angles of the quadrilateral are ( 3 x, 2 x ) and ( x ) respectively.Then, fourth angle ( =3 x+2 x+x=6 x ) Now, sum of all the four angles ( =360^{circ} ) ( therefore quad 3 x+2 x+x+6 x=360^{circ} ) [ Rightarrow ] ( 12 x=360^{circ} ) ( Rightarrow quad x=30^{circ} ) Thus, smallest angle ( =30^{circ} )