Answer :
Answer:
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
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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