Question

the figure below shows a circle with center r, diameter xt, and tangent nd. which of the angles must be right - angles? select all that apply.
answer
∠xrn
∠rne
∠xbo
∠txb
∠trn
∠xon

Explanation:

Step1: Recall circle - tangent property

A radius is perpendicular to the tangent at the point of tangency. Here, $RN$ is a radius and $NDE$ is a tangent, so $\angle RNE = 90^{\circ}$.

Step2: No other information for right - angle determination

There is no information in the problem to suggest that the other angles $\angle XRN,\angle XBO,\angle TXB,\angle TRN,\angle XON$ are right - angles. For example, there is no indication of perpendicular lines for $\angle XRN$; for $\angle XBO$, there is no information about right - angled triangles formed by the chord and other elements; for $\angle TXB$, no perpendicularity is given; for $\angle TRN$, no right - angle relationship is evident; and for $\angle XON$, there is no information suggesting it is a right - angle.

Answer:

$\angle RNE$