Question

DG and EG are tangent to circle C and circle F. The points of tangency are A, B, D, and E. if M

Answer 1

In the circle with center E , DG and EF are tangents at point D and E respectively.

Therefore,

`\angle\text{FEG = }\angle FDG\text{ = 90}_{\text{ }}\text{ \_\_\_\_\_\_\_\_( Radius }\perp\text{ Tangent )}`

In quadrilateral DFEG ,

`\begin{gathered} \angle D\text{ + }\angle F\text{ + }\angle E\text{ + }\angle G\text{ = 360} \\ 90\text{ + 140 + 90 + }\angle G\text{ = 360} \\ \angle G\text{ = 360 - 320} \\ \angle G\text{ = 40} \end{gathered}`

Now,

In the circle with center C , AG and BG are tangents at point A and B respectively.

Therefore,

`\angle\text{CAG = }\angle\text{CBG = 90\_\_\_\_\_\_\_( Radius }\perp\text{ Tangent )}`

In quadrilateral ACBG ,

`\begin{gathered} \angle A\text{ + }\angle C\text{ + }\angle B\text{ + }\angle G\text{ = 360} \\ 90\text{ + 40 + 90 + }\angle C\text{ = 360} \\ \angle C\text{ = 360 - 220} \\ \angle C\text{ = 140} \end{gathered}`

Thus the value of m