Question

For questions 8 – 10, answer the questions about tangent-tangent angles.

Answer 1

m(arc ZWY) = 305°

Explanation:

8). Formula for the angle formed outside the circle by the intersection of two tangents or two secants is,

Angle formed by two tangents =
`(1)/(2)(\text{Difference of intercepted arcs})`

=
`(1)/(2)(220-140)`

=
`(1)/(2)(80)`

= 40°

9). Following the same rule as above,

Angle formed between two tangents =
`(1)/(2)(\text{Difference of intercepted arcs})`

125 =
`(1)/(2)[m(\text{major arc})-m(\text{minor arc})]`

250 =
`[m(\text{arc ZWY})-m(\text{arc ZY})]`

250 = m(arc ZWY) - 55

m(arc ZWY) = 305°

Therefore, measure of arc ZWY = 305° will be the answer.

10). m(arc BAC) =
`(1)/(2)([m(\text{arc BDC})-m(\text{arc BC})])`

=
`(1)/(2)(254-106)`

=
`(148)/(2)`

= 74°