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

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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° .

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