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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.

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JeanaShupp

Answer: The four angles of quadrilateral are [tex]30^{\circ},60^{\circ},150^{\circ}[/tex] and [tex]120^{\circ}[/tex].


Step-by-step explanation:

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

We know that, the sum of all angles of quadrilateral = 360°.

[tex]\Rightarrow\ x+2x+5x+4x=360^{\circ}\\\Rightarrow12x=360^{\circ}\\\Rightarrow\ x=\frac{360}{12}\\\Rightarrow\ x=30[/tex]

Then the first angle [tex]x=30^{\circ}[/tex]

The second angle [tex]2x=2\times30=60^{\circ}[/tex]

The third angle [tex]5x=5\times30=150^{\circ}[/tex]

The fourth angle  [tex]4x=4\times30=120^{\circ}[/tex]

The four angles of the quadrilateral are 30, 60, 150, 120 degrees.

What is quadrilateral?

A quadrilateral is a closed shape and four-sided polygon.

Which have four angles and four corners.

Given

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

The sum of all the interior angles in a quadrilateral is equal to 360 degrees.

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

Then,

[tex]\rm x+2x+5x+4x=360\\\\12x=360\\\\x = \dfrac{360}{12}\\\\x=30[/tex]

Therefore,

The four angles of the quadrilateral are;

x = 30

2x = 2(30) = 60

5x = 5(30) = 150

4x = 4(30) = 120

Hence, the four angles of the quadrilateral are 30, 60, 150, 120 degrees.

To know more about Quadrilateral click the link given below.

https://brainly.com/question/9177423

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