Wendybach5idn
Answered

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A circle is cut into 3 uneven sectors, with angle size: 5x, (9x - 20), & (11x + 5). Find the value of x

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MrRoyalidn

The value of x is 15

Circle

The measure of angles in a circle is 360 degrees.

Sector

The measure of each sector is given as:

[tex]\angle 1 = 5x[/tex]

[tex]\angle 2 = 9x - 20[/tex]

[tex]\angle 3 = 11x + 5[/tex]

Take the sum of the above angles

[tex]\angle 1 + \angle 2 + \angle 3 = 5x + 9x - 20 + 11x + 5[/tex]

Collect like terms

[tex]\angle 1 + \angle 2 + \angle 3 = 5x + 9x + 11x- 20 + 5[/tex]

[tex]\angle 1 + \angle 2 + \angle 3 = 25x-15[/tex]

The sum of the angles is 360.

So, we have:

[tex]25x-15 = 360[/tex]

Add 15 to both sides

[tex]25x = 375[/tex]

Divide both sides by 25

[tex]x = 15[/tex]

Hence, the value of x is 15

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