Question

In the diagram of circle C, m∠VWX is 43°. What is the measure of arc vx?
39°
41°
78°
82°

Answer 1

we know that

The measurement of the external angle is the semi-difference of the arcs which comprises

so

m∠VWX=$\frac{1}{2}(arc\ UY-arc\ VX)$

we have

m∠VWX=$43\°$

$UY=125\°$

substitute the values

$43\°=\frac{1}{2}(125\°-arc\ VX)$

$86\°=(125\°-arc\ VX)$

$arc\ VX=125\°-86\°=39\°$

therefore

the answer is

the measure of arc VX is $39\°$

Answer 2

Based on the circle theorems, the measure of arc vx is: A. 39°

Circle Theorems

• Based on the circle theorems, the external angle formed outside a circle equals half of the difference of the two intercepted arcs of a circle.

Using the circle theorems, we have the following:

m∠VWX = 1/2(measure of arc UY - measure of arc vx)

• Substitute

43 = 1/2(125 - measure of arc vx)

2(43) = 125 - measure of arc vx

86 = 125 - measure of arc vx

measure of arc vx = 39°

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