Question

DG←→ and EG←→ are tangent to circle C and circle F. The points of tangency are A, B, D, and E. If m∠DFE = 140°, what is m∠ACB?

Answer 1

The answer is 140 degrees.

Answer 2

m∠ACB=140°

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°