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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Explanation:

Answer 2

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

Explanation:

Given : The four vertices of an inscribed quadrilateral divide a circle in the ratio 1 : 2 : 5 : 4.

To find : The four angles of the quadrilateral are °, °, °, and °, respectively.

Solution : We have given that The four vertices of an inscribed quadrilateral divide a circle in the ratio 1 : 2 : 5 : 4.

Let the angle of the quadrilateral is x

Then all the angles are x , 2x , 5x ,4x

Complete angle formed by circle is 360 °

Sum of all the angle are 360

x + 2x + 5x + 4x = 360 .

12 x = 360 .

On dividing both sids by 12.

x = 30 .

Then

2x = 60

5x = 5 * 30 = 150 .

4x = 4 *30 = 120 .

Therefore, The four angles of the quadrilateral are 30°, 60°, 150°, and 120°, respectively.