General Idea:
Sum of angles subtended at the centre and point of contact by tangents down from an external point is supplementary (180°).
Applying the concept:
Considering the point of contact of two tangents of large circle, we can write
[tex] \angle DFE+\angle DGE=180 [/tex]
We are given [tex] \angle DFE=140 [/tex], so the equation will become
[tex] 140+\angle DGE=180 [/tex] {Subtracting 140 on both sides}
[tex] 140+\angle DGE -140 = 180 - 140\\ \\ \angle DGE = 40 [/tex]
Considering the point of contact of two tangents of small circle, we can write
[tex] \angle ACB + \angle AGB = 180\\ \\ Note: \angle AGB = \angle DGE = 40\\ \\ \angle ACB + 40 = 180 [/tex]
Subtracting 40 on both sides, we get...
[tex] \angle ACB +40 - 40 = 180 - 40\\ \\ \angle ACB = 140 [/tex]
Conclusion:
[tex] /angle ACB = 40 [/tex]
