Step 1: Understanding angle types
- A right angle is an angle that measures exactly $90^\circ$
- It is formed when two lines intersect to form a perfect L-shape
Step 2: Evaluating the options
(A) $90^\circ$ $\Rightarrow$ This is the correct and exact measure of a right angle
(B) $45^\circ$ $\Rightarrow$ This is an acute angle, less than a right angle
(C) $60^\circ$ $\Rightarrow$ Also an acute angle
(D) $120^\circ$ $\Rightarrow$ An obtuse angle, more than a right angle
\[
\boxed{\text{Correct Answer: (A) } 90^\circ}
\]