Questions and Answers
Which angle pairs are supplementary? (Check all that apply)
What are the special angle pairs in the scenario given?
Which statements are true regarding the given diagram?
What is the measure of ∠EDH if ∠EDH is (5x) degrees and ∠HDG is (4x) degrees?
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What is the measure of ∠CBE if ∠ABC is (3x) degrees and ∠DEF is (2x) degrees?
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What is the measure of ∠B if m∠A = 40° and ∠B is a complement of ∠A?
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What is the measure of ∠C if ∠C is a supplement of ∠B?
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What justifies the statement if ∠CEF is complementary to ∠DCF?
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What can you conclude by the congruent supplements theorem?
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Complete the proof: If 1 and 2 are supplements, and 3 and 2 are supplements, then 1 ___ 3.
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Study Notes
Complementary and Supplementary Angles
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Supplementary Angles: Two angles whose measures add up to 180 degrees.
- Examples from diagrams include pairs ∠4 & ∠3, ∠4 & ∠5, and ∠3 & ∠6.
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Complementary Angles: Two angles whose measures add up to 90 degrees.
- In the examples, ∠ADC & ∠BDC are complementary.
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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.
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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.
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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).
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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°.
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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.
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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.
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Description
Test your understanding of complementary and supplementary angles with this quiz. Explore the relationships between angles, and solve measurement calculations based on given information. Ideal for students studying geometry concepts related to angles.
