the figure below shows a circle with center b, diameter $ \overline{w d} $, secant $ \overleftrightarrow{w e} $, and tangent $ \overleftrightarrow{g x} $. which of the angles must be right angles? select all that apply.
answer
$ \angle b w y $
$ \angle w b g $
$ \angle b w e $
$ \angle b w j $
$ \angle w y d $
$ \angle b g o $

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# Brief Explanations:
- **For $\angle WY D$**:
    - By the Thales' theorem, an angle inscribed in a semicircle is a right - angle. Since $\overline{WD}$ is a diameter and $Y$ is on the circle, $\angle WY D = 90^{\circ}$.
 - **For $\angle BGO$**:
    - A tangent to a circle is perpendicular to the radius at the point of tangency. $\overleftrightarrow{GX}$ is a tangent and $\overline{BG}$ is a radius, so $\angle BGO=90^{\circ}$.
 - **For $\angle BWJ$**:
    - A tangent to a circle is perpendicular to the radius at the point of tangency. $\overleftrightarrow{GX}$ is a tangent and $\overline{BW}$ is a radius, so $\angle BWJ = 90^{\circ}$.

# Answer:
$\angle WY D,\angle BGO,\angle BWJ$

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