Answer:
m∠ACB=140°
Step-by-step explanation:
Given: DG and EG are tangent to circle C and circle F. The points of tangency are A, B, D, and E and m∠DFE = 140°.
To find: m∠ACB
Solution: Angle E is made between a tangent and a chord, thus its measure is equal to 90°, similarly the measure of angle B will be equal to 90°.
Now, consider the quadrilateral GEFD and using the angle sum property of the quadrilateral, we have
∠E+∠F+∠D+∠G=360°
⇒90°+140°+90°+∠G=360°
⇒∠G+320°=360°
⇒∠G=40°
Now, consider the quadrilateral GBCA and using the the angle sum property of the quadrilateral, we have
∠B+∠C+∠A+∠G=360°
⇒90°+∠C+90°+40°=360°
⇒∠C+220°=360°
⇒∠C=140°
Thus, the measure of angle ACB=140°
