Question

The figure below shows a circle with center Z, diameter start overline, F, K, end overline
FK
, and secant F, E, with, left-right arrow, on top
FE
. Which of the angles must be right angles? Select all that apply. A. ∠NFZ
B. angle, F, N, K∠FNK
C. angle, Z, F, E∠ZFE
D. angle, Z, F, G∠ZFG
E. angle, N, F, E∠NFE
F. angle, N, F, G∠NFG

Answer 1

B only.

Reason: By Thales' theorem an angle with endpoints at the ends of a diameter is a right angle. ∠FNK subtends diameter FK at point N on the circle, so it must be 90°. The other listed angles are not necessarily right from the given information.