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Understanding Angles: Vertical, Linear Pairs, and Calculating Measures

This lesson covers types of angles including obtuse, acute, and straight angles, explaining their properties and relationships. It highlights key concepts like vertical angles, which are congruent, and linear pairs, which are adjacent angles that sum to 180 degrees. Through examples and exercises, students will learn to calculate angle measures and solve for variables in angle relationships. The material also emphasizes understanding the relationships between angles, providing a solid foundation for further geometrical concepts.

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Understanding Angles: Vertical, Linear Pairs, and Calculating Measures

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  1. Week 2 Warm Up 08.26.11 P • • • • Q S T R 1) Name an Obtuse angle? 2) Acute angle? 3) Straight angle?

  2. Their sides form two pairs of opposite rays. Vertical angles are congruent. Vertical Angles Ex 1 1 2 4 3 ∠4 and ∠2 are vertical angles ∠3 and ∠1 are vertical angles ∠4 ≅ ∠2 ∠3 ≅ ∠1 m∠4 = m∠2 m∠3 = m∠1

  3. 2 Ex 2 150º if the m∠1 = 150º, then the m∠2 = _____ ∠1 and ∠2 are vertical angles 1 ∠1 ≅ ∠2 m∠1 = m∠2 150º = ∠2

  4. Ex 3 P Find the Variable ∠QPR and ∠TPS are vertical angles ∠QPR ≅ ∠TPS • • • • T S Q R ( 7x – 10 )⁰ m∠QPR = m∠TPS 7x – 10 = 2x + 55 ( 2x + 55 )⁰ 7x - 2x – 10 = 55 5x – 10 = 55 5x = 55 + 10 5x = 65 x = 13

  5. Linear Pairs Linear Pair angles are adjacent angles that add up to 180º and their noncommon sides are opposite rays. Ex 4 1 2 ∠1 and ∠2 are linear pairs m∠1 + m∠2 = 180º

  6. Ex 5 25º 1 2 ∠1 and ∠2 are linear pairs m∠1 + m∠2 = 180º m∠1 + 25º = 180º m∠1 = 180º - 25º m∠1 = 155º

  7. ( 3x + 33 )º Ex 6 ( 2x – 13 )º linear pairs 2x – 13 + 3x + 33 = 180 5x + 20 = 180 5x = 180 - 20 5x = 160 x = 32

  8. x = 32 2x – 13 3x + 33 2( 32 ) – 13 3( 32 ) + 33 96 + 33 64 – 13 129º 51º 51º + 129º = 180º

  9. Ex 7 7 35º if the m∠6 = 145º, then the m∠7 = _____ ∠6 and ∠7 are linear Pairs m∠6 + m∠7 = 180º 6 145º + m∠7 = 180º m∠7 = 180º - 145º m∠7 = 35º

  10. Textbook page 48, 23 – 30 all Quiz :

  11. Review Linear pairs add up to ______º. P Do 1: • • • • Q S T R ( 9x – 6 ) ( 7x + 6 ) Textbook page 48, 24 – 33 all Quiz :

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