Question

In circle o, mFG = 30°, mBC = 120, and ZJ CZKBEF30°K140°120°HсWhat is mEH?35°40°45°50°

Answer 1

According to the intersecting secant theorem, we have that:

`\angle J=(1)/(2)*(mBC-mFG)`

and likewise:

`\angle K=(1)/(2)*(mAD-mEH)`

Since we have that:

`\begin{gathered} mBC=120 \\ mFG=30 \end{gathered}`

we can get
`\angle J=(1)/(2)*(120-30)`
`\angle J=(1)/(2)*(90)`
`\angle J=45`Now, since we have that:

`\begin{gathered} mAD=140 \\ \angle K=\angle J=45 \end{gathered}`

We can obtain mEH, as follows:

`\begin{gathered} \angle K=(1)/(2)*(mAD-mEH) \\ \end{gathered}`
`45=(1)/(2)*(45-mEH)`
`45*2=140-mEH`
`90=140-\text{mEH}`
`\text{mEH}=140-90`

`\text{mEH}=50`

Thus, correct answer: option D