Question

If mAC 93°, and mBD= 39°, what is m∠BED? 54° 32° 108° 27°

Answer 1

Answer: LAST OPTION.

Step-by-step explanation:

For this exercise it is important to remember that, by definition, the angle formed by two secants intersecting outside of a circle, can be found with the following formula:

$Angle\ formed\ by\ two\ secants=\frac{Difference\ of\ intercepted\ arcs}{2}$

According to the information provided in the exercise, you know that:

$mAC= 93\°\\\\mBD= 39\°$

Therefore, you can find the difference of the intercepted arcs:

$Difference\ of\ intercepted\ arcs=93\°-39\°\\\\Difference\ of\ intercepted\ arcs=54\°$

The final step is to substitute  the difference of the intercepted arcs calculated above, into the formula, in order to find the measure of the angle  BED.

You get that this is:

$Angle\ formed\ by\ two\ secants=\frac{54\°}{2}\\\\Angle\ formed\ by\ two\ secants=27\°$