Multiple choice problem

Question

If the measure of angle 1 is 35^o, and the measure of is 22^o, then what is the measure of ?

112

92

85

68

None of these.

Answer 1

The measure of an angle formed outside a circle of two secants = 1/2 difference of measures of intercepted arcs so:

m<1 = 1/2 (m(VU) - m(ST)

35 = 1/2 (m(VU) - 22)

70 = m(VU) - 22

92 = m(VU)