Question

the figure below shows a circle with center s, diameter lj, secant li, and tangent fz. which of the angles must be right - angles? select all that apply.
answer attempt 2 out of 2
∠fjs
∠sfx
∠flk
∠lsf
∠lfj
∠lfx

Explanation:

Step1: Recall circle - tangent property

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

Step2: Analyze each angle

• $\angle FJS$: There is no reason for this angle to be a right - angle as there is no special geometric relationship (like diameter - subtended angle or radius - tangent relationship) indicating it is 90 degrees.
• $\angle SFX$: Since $FX$ is a tangent and $SF$ is a radius, by the property that a tangent to a circle is perpendicular to the radius at the point of tangency, $\angle SFX = 90^{\circ}$.
• $\angle FLK$: There is no geometric property that makes this angle a right - angle.
• $\angle LSF$: There is no special geometric relationship (such as a diameter - subtended angle or a radius - tangent relationship) that makes this angle 90 degrees.
• $\angle LFJ$: There is no reason for this angle to be a right - angle.
• $\angle LFX$: There is no geometric property that makes this angle a right - angle.

Answer:

$\angle SFX$