Question

Determine the measure of ∠BFE.Question options:1) 112°2) 111°3) 69°4) 224°

Answer 1

`x\text{ = 5 (option 3)}`

Step-by-step explanation:

We apply tangent-tangent theorem:

`\begin{gathered} one\text{ tangeht = 9} \\ 2nd\text{ tangent = 2x - 1} \end{gathered}`

The tangent segement from the same external points are congruent:

`9\text{ = 2x - 1}`
`\begin{gathered} Add\text{ 1 to both sides:} \\ 9\text{ + 1 = 2x} \\ 10\text{ = 2x} \\ \text{divide both sides by 2:} \\ (10)/(2)\text{ = }(2x)/(2) \\ x\text{ = 5} \end{gathered}`