The angles having the same measure are called the congruent angles.

The concept of congruent angles was introduced in mathematics by considering the meanings of two words “congruent” and “angle”.

- The word “Congruent” means equal.
- The word “Angle” means the amount of rotation.

An angle between two sides in an object can be measured geometrically. In a special case, an angle of an object can be exactly equal to the angle of another object, and such angles of two or more objects are called the congruent angles.

Alternatively, the congruent angles are also called as the equal angles in mathematics.

Now, let’s learn the concept of the congruent angles by an understandable example.

Look at the picture and observe the two geometric figures in it.

- The left side geometric figure expresses the angle $\small BAC$ and its angle is measured as forty degrees.
- The right side geometric figure expresses the angle $\small QPR$ and its angle is measured as forty degrees.

The $\small \angle \, BAC \,=\, 40^\circ$ and the $\small\angle \, QPR \,=\, 40^\circ$. According to the these two mathematical equations, we can understand that the angle $\small BAC$ is equal to the angle $\small QPR$. So, the angle $\small BAC$ is congruent to the angle $\small QPR$.

The equality of the both angles $\small BAC$ and $\small QPR$ can be mathematically expressed as follows.

$\therefore\,\,\,\,\,\,$ $\small \angle \, BAC \,\cong\, \angle \, QPR$

Therefore, the $\small \angle \, BAC$ and $\small \angle \, QPR$ are called the congruent angles, and they are also called as the equal angles.

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