Question

the angles of a quadrilateral are in the ratio 2 is to 3 is to 4 is to 6 find the measure of the each of the four angles

Answer 1

According to question

Ration of two angles of quadrilateral

A : B = 2 : 3
Thus  
A = 2x
and   B = 3x

Also Ratio of another two angles

C : D = 4 : 6
Thus

C = 4x
nd   D = 6x

We know
In  Quadrilateral
A + B + C + D = 360 deg
Thus

2x + 3x +  4x + 6x = 360
15x  = 360
Thus  x = 24

So    A = 2 * 24 = 48 deg
        B = 3 * 24 = 72 deg
        C = 4 * 24 = 96 deg
and  D = 6 * 24 = 144 deg

Answer 2

The ratio of the angles is 2:3:4:6

To find: The measures of each angle.

Observe that 2+3+4+6=15.

Thus 15 parts accounts for 360⁰

Hence, 15 parts = 360⁰

2 parts = ( 360⁰/15)× 2 = 48⁰

3 parts = (360⁰/15)× 3 = 72⁰

4 parts = ( 360⁰/15)× 4 = 96⁰

6 parts = ( 360⁰/15)× 6 = 144 ⁰

Thus the angles are 48 72⁰ , 96⁰ 144⁰