Complementary and Supplementary Angles Quiz

Complementary and Supplementary Angles

• Supplementary Angles: Two angles whose measures add up to 180 degrees.

  • Examples from diagrams include pairs ∠4 & ∠3, ∠4 & ∠5, and ∠3 & ∠6.

• Complementary Angles: Two angles whose measures add up to 90 degrees.

  • In the examples, ∠ADC & ∠BDC are complementary.

• Right Angles: Commonly occur where two lines intersect at a 90-degree angle.

  • In the intersection of horizontal and vertical lines, ∠GNH & ∠HNJ are complementary angles.

• Angle Relationships:

  • In cases where angles are formed by intersecting lines, the sum of the angles on a straight line equals 180 degrees.
  • For instance, m∠HNK + m∠KNL = 180° demonstrates this relationship.

• Measurement Calculation:

  • From problems, angles can often be expressed as multiples (e.g., ∠EDH is calculated as 50 degrees, given ∠EDH = 5x and ∠HDG = 4x).
  • Similarly, for angles ACB and DEF, relationships can be established to find exact measures, leading to ∠CBE = 72° (where ∠ABC = 3x and ∠DEF = 2x).

• Definitions:

  • Complement of an angle (∠B) is found through the equation m∠A + m∠B = 90°.
  • If an angle is a supplement (∠C) to another angle, the relation is defined as m∠B + m∠C = 180°.

• Theorems and Properties:

  • Congruent Supplements Theorem: If angles are supplementary to the same angle, they are congruent.
  • Proofs often apply substitution to demonstrate angle relationships, such as proving that if angles 1 and 2 are supplements, and angles 3 and 2 are supplements, then angles 1 and 3 must also be supplements based on their measurements relating back to angle 2.

• Practical Examples and Test Questions:

  • Problems may require identifying angle pairs from given diagrams and applying definitions and properties to find measures or relationships between angles.
  • Key calculations often involve substituting angle expressions and solving equations to find unknown angles.