Urgent ! 20 ! find arc bc + arc ad i figured out that x=6 i just can't figure out what the any of the angles measures are!.

x = 6 is correct

Focus on the right triangle EDF. The short leg is x = 6. The hypotenuse is 4+8 = 12. Since the hypotenuse is twice that of the short leg, we have a 30-60-90 triangle. Recall that the ratio of the short leg, long leg and hypotenuse is 1:sqrt(3):2 or you can think of it as x: x*sqrt(3): 2x. The 30 degree angle is opposite the short leg (smallest angle opposite smallest side). So the 60 degree angle is angle FED, which is the angle formed by the two chords.

This means angle BEC is 120 degrees since 120+60 = 180.

Now use the second part of the hint which says that the two arcs add up and are cut in half to get the angle formed by the intersecting chords. This means,

angle BEC = (1/2)*(arc BC + arc AD)

120 = (1/2)*(arc BC + arc AD)

2*120 = 2*(1/2)*(arc BC + arc AD)

240 = arc BC + arc AD

arc BC + arc AD = 240 degrees

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.

what