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Understanding Angles: Definitions, Relationships, and Algebraic Expressions

Explore the world of angles through various concepts including vertical, supplementary, and complementary angles. Learn to simplify algebraic expressions and create algebraic expressions based on verbal descriptions of angle relationships. This guide includes practical problems such as finding the measure of angles given certain conditions, determining complements and supplements, and identifying angle types. Perfect for students looking to strengthen their understanding of angle relationships and enhance their algebraic skills.

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Understanding Angles: Definitions, Relationships, and Algebraic Expressions

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  1. Angle Relationships Section 1.7

  2. Warm Up Simplify each expression. 1.90 –(x + 20) 2. 180 – (3x – 10) Write an algebraic expression for each of the following. 3. 4 more than twice a number 4. 6 less than half a number

  3. Vertical Angles: Two non adjacent angles formed by two intersecting lines.

  4. Name: • Adjacent ∠’s • 2. Linear pairs • 3. Vertical ∠’s

  5. What is the relationship.

  6. Supplementary Angles • Angles that add up to 180 degrees.

  7. Complementary Angles • Angles that add up to 90 degrees.

  8. Find the measure of each of the following. A. complement of F B. supplement of G

  9. Find the measure of each of the following. a. complement of E b. supplement of F

  10. Find x and MEASURE OF ∠AZD

  11. Find x and MEASURE OF ∠AZD

  12. Gh AND jk INTERESECT AT i. FIND THE VALUE OF X AND M∠JIH.

  13. Gh AND jk INTERESECT AT i. FIND THE VALUE OF X AND M∠gik.

  14. FIND M∠egf

  15. FIND x and THE M∠cde.

  16. FIND the MEASURE of each angle. 1. ∠ SOT 2. ∠ POU 3. ∠ ROS 4. ∠ POR 5. ∠ SOU 6. ∠ TOU 7. ∠ POS 8. ∠ UOQ

  17. A. Name 2 pairs of vertical angles. • B. If ray BF bisects ∠ABC, what two angles must be equal. • C. Classify each as acute, obtuse, right or straight. • 1. ∠BAF • 2. ∠FCE • 3. ∠BFA

  18. An angle is 10° more than 3 times the measure of its complement. Find the measure of the complement.

  19. An angle’s measure is 12° more than the measure of its supplement. Find the measure of the angle.

  20. Lesson Quiz: Part I • mA= 64.1°, and mB=(4x – 30)°. Find the measure of each of the following. • supplement of A • 2. complement of B • 3. Determine whether this statement is true or false. If false, explain why. If two angles are complementary and congruent, then the measure of each is 90°.

  21. mXYZ = 2x° and mPQR = (8x - 20)°. 4. If XYZ and PQR are supplementary, find the measure of each angle. 5. If XYZ and PQR are complementary, find the measure of each angle.

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