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___°

First blank
45 or 85
Second blank
75 or 90
Third blank
115 or 135
Fourth blank
105 or 125

Answer 1

Let the angles be

1x , 2x , 5x and 4x

as the sum of the angles of a quadrilateral is 360°,

=> 1x + 2x + 5x + 4x = 360°

or

12x = 360°

=> x = 360/12 = 30

=> x = 30

or

1x = 1× 30 = 30°

2x = 2 × 30 = 60°

5x = 5 × 30 = 150°

4x = 4 × 30 = 120°

Hence the angles of the quadrilateral are

30° , 60° , 150° , 120° .

I hope this helped

Chris