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.
<h3>What is quadrilateral?</h3>
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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