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Name the angle in 4 different ways _____, _____, _____, & _____ Name the vertex . ____

Name the angle in 4 different ways _____, _____, _____, & _____ Name the vertex . ____ Name the sides . ____ Find its measure . ____ Shade its interior. G. A. 1. N. 2a. Definition for complementary angles 2b. Examples of complementary angles:.

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Name the angle in 4 different ways _____, _____, _____, & _____ Name the vertex . ____

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  1. Name the angle in 4 different ways _____, _____, _____, & _____ Name the vertex. ____ Name the sides. ____ Find its measure. ____ Shade its interior. G A 1 N

  2. 2a. Definition forcomplementary angles 2b. Examples of complementary angles: The measures of two angles are said to be complementary if and only if the sum of the measures is 90 A B 50◦ 30◦ 40◦ 1 60◦ 2 C D 1 and 2 are adjacent & complementary A &D are non-adjacent & complementary B &C are non-adjacent & complementary

  3. Numeric Find the measure of each angle. Verbal m1 = 24 m2 = 3(24) – 6 = ? 66 Algebraic Set up an solve an equation Graphic Use a protractor to draw the angles to scale. m1 = x m2 = 3x - 6 24 x + 3x – 6 = 90 4x – 6 = 90 4x = 96 x = 24

  4. 3a. Definition forsupplementary angles 3b. Examples of supplementary angles: The measures of two angles are said to be supplementary if and only if the sum of the measures is 180 A B C 150◦ 120◦ 30◦ 1 2 60◦ D 1 and 2 are adjacent & supplementary A &B are non-adjacent & supplementary C &D are non-adjacent & supplementary

  5. Verbal Numeric Find the measure of each angle. m1 = 14 m2 = 8(14) + 54 = ? Algebraic Set up an solve an equation 166 Graphic Use a protractor to draw the angles to scale. m1 = x m2 = 8x + 54 x + 8x + 54 = 180 9x + 54 = 180 9x = 126 x = 14

  6. 4.

  7. 5a. Definition forlinear pair 5b. Proof involving linear pair Two adjacent angles form a linear pair if and only if their non-common sides are opposite rays D B A C Ray AB & ray AC are opposite rays, which unite to make a straight angle, therefore mCAB = 180. By angle addition: mCAD + mDAB = mCAB = 180 mCAD + mDAB = 180

  8. Linear Pair Theorem If two angles form a linear pair, then they are supplementary.

  9. 6a. Definition for vertical angles: 6b. Proof involving vertical angles Two non-straight angles are vertical angles if and only if the union of their sides is two lines. C O B A D Because they form a linear pair, mAOC + mCOB = 180 AB U CD AOC and BOD are supplements to the same angle so they must have the same measure can be described as AOC & BOD. & m COB + mBOD = 180

  10. Vertical Angles Theorem If two angles are , vertical angles then they have equal measures.

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