Question

The four vertices of an inscribed quadrilateral divide a circle in the ratio 1 : 2 : 5 : 4. The four angles of the quadrilateral are °, °, °, and °, respectively.

Answer 1

Answer: The four angles of quadrilateral are $30^{\circ},60^{\circ},150^{\circ}$ and $120^{\circ}$.

Step-by-step explanation:

Let the sides of quadrilateral be x, 2x, 5x and 4x.

We know that, the sum of all angles of quadrilateral = 360°.

$\Rightarrow\ x+2x+5x+4x=360^{\circ}\\\Rightarrow12x=360^{\circ}\\\Rightarrow\ x=\frac{360}{12}\\\Rightarrow\ x=30$

Then the first angle $x=30^{\circ}$

The second angle $2x=2\times30=60^{\circ}$

The third angle $5x=5\times30=150^{\circ}$

The fourth angle  $4x=4\times30=120^{\circ}$

Answer 2

quadrilateral, sum of interior angles = 360

ratio 1 : 2 : 5 : 4
so 1+2+5+4 = 12

360 / 12 = 30

1 x 30 = 30
2 x 30 = 60
5 x 30 = 150
4 x 30 =120


answer 

The four angles of the quadrilateral are 30,60,150 and 120