Question

Select the correct answer from each drop-down menu. 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 °.

Answer 1

The four angles of a quadrilateral are  30°, 60°, 150°, and 120°  if the four vertices of an inscribed quadrilateral divide a circle in the ratio 1:2:5:4.

What is quadrilateral?

It is defined as the four-sided polygon in geometry having four edges and four corners.

We have the four vertices of an inscribed quadrilateral divide a circle in the ratio:

1:2:5:4

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

We know the sum of all angles of quadrilateral = 360°

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

12x = 360

First angle, x = 30°

Seconds angle, 2x = 2×30 ⇒ 60°

Third angle, 5x = 5×30 ⇒ 150°

Fourth angle, 4x = 4×30 ⇒ 120°

Thus, the four angles of a quadrilateral are  30°, 60°, 150°, and 120°

Learn more about the quadrilateral here:

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