Identify complementary, supplementary, vertical, adjacent and congruent angles

Key notes:

1. Angles and Their Types

a. Complementary Angles

  • Definition: Two angles are complementary if their measures add up to 90 degrees.
  • Example: If one angle measures 30 degrees, the complementary angle measures 60 degrees (30° + 60° = 90°).

b. Supplementary Angles

  • Definition: Two angles are supplementary if their measures add up to 180 degrees.
  • Example: If one angle measures 110 degrees, the supplementary angle measures 70 degrees (110° + 70° = 180°).

c. Vertical Angles

  • Definition: Vertical angles are the angles opposite each other when two lines intersect. They are always equal.
  • Example: If two lines intersect and form angles of 45 degrees and 45 degrees, these angles are vertical angles.

d. Adjacent Angles

  • Definition: Adjacent angles are two angles that share a common vertex and a common side but do not overlap.
  • Example: When two angles of 30 degrees and 50 degrees share a side, they are adjacent angles.

e. Congruent Angles

  • Definition: Congruent angles are angles that have the same measure.
  • Example: If two angles measure 70 degrees each, they are congruent angles.

Learn with an example

📢 Which angle is adjacent to ∠CFD?

  • ∠BFD
  • ∠DFA
  • ∠EFA
  • ∠AFB

Look at ∠CFD and ∠DFA:

∠DFA is adjacent to ∠CFD.

📢 Which angle is complementary to ∠2?

  • ∠3
  • ∠6
  • ∠4
  • ∠5

Look at ∠2 and ∠4:

∠4 is complementary to ∠2. First, notice that ∠2 and ∠1 are complementary. Along with the right angle, they form a straight line. The straight line measures 180° and the right angle measures 90°. That leaves another 90°, so ∠2 and ∠1 have measures that add up to 90°. Next, notice that ∠1 and ∠4 are vertical angles. That means they have the same measure. Since ∠2 and ∠1 are complementary, ∠2 and ∠4 are also complementary. Their angles add up to 90°.

📢 Which angle is complementary to ∠3?

  • ∠5
  • ∠2
  • ∠4
  • ∠6

Look at ∠3 and ∠4:

∠4 is complementary to ∠3. Along with the right angle, they form a straight line. The straight line measures 180° and the right angle measures 90°. That leaves another 90°, so ∠3 and ∠4 have measures that add up to 90°.

Let’s practice!🖊️