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:

$\angle J=\frac{1}{2}\times(mBC-mFG)$

and likewise:

$\angle K=\frac{1}{2}\times(mAD-mEH)$

Since we have that:

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

we can get $\angle J=\frac{1}{2}\times(120-30)$$\angle J=\frac{1}{2}\times(90)$$\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=\frac{1}{2}\times(mAD-mEH) \\ \end{gathered}$$45=\frac{1}{2}\times(45-mEH)$$45\times2=140-mEH$$90=140-\text{mEH}$$\text{mEH}=140-90$

$\text{mEH}=50$

Thus, correct answer: option D