**Correct option is (D) 45°**

If an angle of \(90^\circ\) is to be bisected.

Then each obtained angles \(=\frac{90^\circ}2=45^\circ.\)

**Alternative :- **Let angles x & y are angles which is obtained by bisecting an angle of \(90^\circ.\)

\(\therefore\) x = y and x+y = \(90^\circ.\) \((\because\) Both angles obtained by bisecting an angle of \(90^\circ)\)

\(\Rightarrow\) 2x = 2y = \(90^\circ\)

\(\Rightarrow\) \(x=y=\) \(\frac{90^\circ}2=45^\circ\)