Question

the figure below shows a circle with center i, diameter ie, and tangents es and cq. which of the angles must be right angles? select all that apply. answer
∠ics
∠ces
∠iea
∠tce
∠cse

Explanation:

Step1: Recall tangent - radius property

A tangent to a circle is perpendicular to the radius at the point of tangency.

Step2: Analyze angles related to tangents

Since $ES$ is a tangent and $IE$ is a radius (with $E$ being the point of tangency), $\angle IES = 90^{\circ}$. Also, since $CQ$ is a tangent and $IC$ is a radius (with $C$ being the point of tangency), $\angle ICS=90^{\circ}$.

Answer:

$\angle ICS$, $\angle CES$ (because $\angle IES = 90^{\circ}$ and $\angle CES$ is part of the right - angled $\angle IES$ considering the line $ES$ and the angles formed at $E$)