Congruent Angles

Congruent angles are two or more angles with equal measures in degrees as well as in radians. The direction or length of the lines does not make any difference on congruency.

congruent angles

We know that all angles in an equilateral measure the same; that is 60°.

congruent angles

So, the angles in an equilateral triangle are congruent angles.

Example: If line CD bisects another line AB at the point O, then which of the following is true?

congruent angles

A) ∠AOB ≅ ∠AOD

B) ∠COB  ≅ ∠BOD

C) ∠AOD  ≅ ∠COB

D) ∠COD  ≅ ∠AOC

∠AOD  ≅ ∠COB as these are vertically opposite angles and hence their measure is the same.




  1. Which are the congruent angles in the given triangles?
congruent angles

2. What is the value of x if the given two angles are congruent?

congruent angles

3.Find the value of b.

congruent angles

4.What is the value of x, if in the given triangles, ∠ABC ≅ ∠RPQ?

congruent angles

  5.Do congruent angles measure the same in degrees and radians?

Answer key
  1. ∠ACB ≅ ∠PRQ
  2. 34
  3. 40°
  4. 47°
  5. Yes