Classifying Angles

Angles are classified according to their angle measure. The main types are acute angle, right angle, obtuse angle, and straight angle. These are shown in the figure below. 

Adjacent Angles

Two angles are Adjacent when they have a common side and a common vertex and do not overlap. In the figure below, angle ABD is adjacent to angle CBD. The reason is that they have a common side (line BD), and they have a common vertex (point B). Note that angle ABC is 90 degrees and angles ABD, and CBD are complementary.

Congruent Angles

Two angles are congruent if they have the same measure or are open the same amount. The angles do not have to have congruent sides or face the same direction.

In the figure above, angle ABC is congruent to angle PQR because they both measure 53 degrees.

Other examples of congruent angles are shown below.

Solve the following problems

Worked example.  In question 1, ,angle PQR is 90 degrees, and angle BQR is 54.5 degrees. Then angle PQB is 90 – 54.5 = 35.5.

2. Find the missing angle measurement in each set of complementary angles

3. Match the Congruent Angles