Question

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

Answer 1

Answer:

m(arc ZWY) = 305°

Step-by-step 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 = $\frac{1}{2}(\text{Difference of intercepted arcs})$

                                                   = $\frac{1}{2}(220-140)$

                                                   = $\frac{1}{2}(80)$

                                                   = 40°

9). Following the same rule as above,

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

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

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) = $\frac{1}{2}([m(\text{arc BDC})-m(\text{arc BC})])$

                          = $\frac{1}{2}(254-106)$

                          = $\frac{148}{2}$

                          = 74°