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The value of x from the given figure is 6.

Geometry is a branch in mathematics used in the measurement of angles, lines and properties of solids.

To get the value of x from the diagram shown, we will use the theorem which states that "the angle at the vertex <WVU is equal to half the difference of angles at the intercepted arcs".

Mathematically, this is expressed as:

<WVU = 1/2(major arcs - minor arcs)

Major arc = 37x + 5

Minor arc = 23x - 5

<WVU = 1/2 [(37x + 5 - (23x - 5)]

5x + 17 = 1/2 [(37x + 5 - (23x - 5)]

5x + 17 = 1/2 (37x + 5 - 23x + 5)

5x + 17 = 1/2 (14x + 10)

Cross multiply

2(5x + 17) = 14x + 10

Expand

10x + 34 = 14x + 10

Collect the like terms

10x - 14x = 10 - 34

-4x = -24

Divide both sides by -4

-4x/-4 = -24/-4

x = 6

Hence the value of x from the given figure is 6.

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x = 6

Step-by-step explanation:

∠WVU lies outside the circle and the sides are tangents. The measure of the tangent- tangent angle is

∠WVU = 0.5( major arc - minor arc), that is

5x + 17 = 0.5(37x + 5 - (23x - 5)) = 0.5(37x + 5 - 23x + 5) = 0.5(14x + 10), so

5x + 17 = 7x + 5 ( subtract 7x from both sides )

- 2x + 17 = 5 ( subtract 17 from both sides )

- 2x = - 12 ( divide both sides by - 2 )

x = 6

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step-by-step explanation: