Question

∠ABC is formed by two tangents intersecting outside of a circle. If minor arc AC = 110°, what is the measure of ∠ABC?

Answer 1

The answer to this problem is 70. Hope I helped :)

Answer 2

∠ABC = 70°

Explanation:

As shown in the figure attached AB and BC are two tangents drawn on a circle touching at A and C.

Measure of minor arc = 110°

And we have to find the measurement of ∠ABC.

Since measure of minor arc AC = 110°

and m(minor arc AC) + m(major arc AC) = 360°

110° + major arc AC = 360°

major arc AC = 360 - 110 = 250°

and angle formed outside the circle by two tangents formed at B = 1/2(difference of intercepted arcs)

=
`(1)/(2)(major arc - minor arc)=(1)/(2)(250-110)=(1)/(2)(140)=70`

Therefore answer is ∠ABC = 70°