Since you are looking for an angle congruent to <UQR using the alternate interior angles theorem, interior suggests that the angle must be inside the parallel lines, se we can get rid of options <WRT and <TRZ since they are exterior angles
Furthermore, in the alternate interior angles theorem, the two angles must be alternate or opposite of each other which would show that the only possible answer would be <QRZ
Write the left side of the given expression as N/D, where N = sinA - sin3A + sin5A - sin7A D = cosA - cos3A - cos5A + cos7A Therefore we want to show that N/D = cot2A.
We shall use these identities: sin x - sin y = 2cos((x+y)/2)*sin((x-y)/2) cos x - cos y = -2sin((x+y)/2)*sin((x-y)2)
