Answer:
∠ABC = 70°
Step-by-step 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)
=[tex]\frac{1}{2}(major arc - minor arc)=\frac{1}{2}(250-110)=\frac{1}{2}(140)=70[/tex]
Therefore answer is ∠ABC = 70°
