Question

the figure below shows a circle with center n, diameter by, and tangent xv. which of the angles must be right angles? select all that apply. answer
∠bnx
∠xyn
∠yxs
∠bxs
∠nxs

Explanation:

Step1: Recall tangent - radius property

A tangent to a circle is perpendicular to the radius at the point of tangency. Here, $XV$ is tangent to the circle with center $N$ at point $X$. So, $\angle NXV = 90^{\circ}$. Also, since $\angle NXS$ and $\angle NXV$ are the same angle, $\angle NXS$ is a right - angle.

Step2: Analyze other angles

There is no information or geometric property that would make $\angle BNX$, $\angle XYN$, $\angle YXS$, $\angle BXS$ right - angles. $\angle BNX$ is a central angle, $\angle XYN$ is an inscribed angle, and $\angle YXS$ and $\angle BXS$ are not related to the right - angle - creating geometric relationships in this context.

Answer:

$\angle NXS$