Question

Which equation can be solved to find x, the measure of BD in the diagram below?

Answer 1

The rule for the angle formed outside of circle by intersection show below is given by:
Angle formed outside=1/2(difference of intercepted arcs)
∠ACE=1/2(AE-BD)
∠ACE=53°
AE=233°
BD=x
Hence the formula for obtaining BD will be:
53=1/2(233-x)
The correct answer is A

Answer 2

Answer:

A. $\frac{1}{2} (233^{o}-x)=53^{o}$

Step-by-step explanation:    

Let x be the measure of arc BD.

Since we know that an angle formed by two intersecting tangents equals one-half the difference of the measures of the intercepted  arcs (the major arc-minus the minor arc).  

$\text{ Measure of tangent-tangent angle}=\frac{1}{2} (\text{measure of major arc-measure of minor arc})$

We can see from our given graph that the tangent-tangent angle's measure is 53 degree. The measure of its intercepting major arc equals 233 degrees and minor arc equals x.

Upon substituting our given values in above formula we will get,

$53^{o}=\frac{1}{2} (233^{o}-x)$

$\frac{1}{2} (233^{o}-x)=53^{o}$

Therefore, the equation that can be solved to find x (the measure of arc BD) will be $\frac{1}{2} (233^{o}-x)=53^{o}$ and option A is the correct choice.