The figure shows secant GC and tangent GB intersecting to form an angle. Find x and y If necessary, round to the tenths place.

Question

The figure shows secant GC and tangent GB  intersecting to form an angle. Find x and y  If necessary, round to the tenths place.

anonymous · Answer

attachment

imstuck · Answer

y is equal to half the measure of the arc it intercepts.  What is the measure of the arc angle y intercepts?

anonymous · Answer

93?

imstuck · Answer

Does that circle have a center A?

anonymous · Answer

yes i believe so

imstuck · Answer

Ok, let's back up here for just a minute.  There's a lot going on with this circle.  first of all, let's find the measure of the missing arc, arc DB.  What is that?

anonymous · Answer

would that be 66?

imstuck · Answer

yes it would.  So now that we have that, we can find out the measure of angle C.  Angle C is an inscribed angle that intercepts arc DB.  Do you know the measure of angle C if it's an inscribed arc and it intercepts an arc measuring 66?

anonymous · Answer

would that be 90-66

imstuck · Answer

An inscribed angle measures half of its intercepted arc.  If the arc is 66, then what would the angle be?

anonymous · Answer

33

imstuck · Answer

Now let's find D in much the same way.  D is inscribed also and is equal to half the measure of the arc it intercepts.  Angle D intercepts arc CE which has a measure of 81.  So what is the measure of angle D if it measures half of its intercepted arc of 81?

anonymous · Answer

40.5?

nikato · Answer

theres an easier way.

these would be the formula you would use

|dw:1402965421648:dw|