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Pairs of Angles

Pairs of Angles. Geometry (Holt 1-4) k.Santos. Adjacent Angles. Adjacent angles—two angles in the same plane (coplanar) with a common vertex , a common side but no common interior points A D B C < ABD and <DBC are adjacent angles.

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Pairs of Angles

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  1. Pairs of Angles Geometry (Holt 1-4) k.Santos

  2. Adjacent Angles Adjacent angles—two angles in the same plane (coplanar) with a common vertex, a common side but no common interior points A D B C < ABD and <DBC are adjacent angles

  3. Linear Pair Linear Pair—a pair of adjacent angles whose noncommon sides are opposite sides 1 2 < 1 and < 2 form a linear pair

  4. Complementary Angles Complementary Angles—two angles whose measures have a sum of 90 A D 30 60 B C Adjacent and non-adjacent and Complementary complementary <ABD and <DBC 30= 90

  5. Example---Complementary angles Given: m< 1 =3x + 7 and m < 2= 7x + 3. Find x, m< 1 and m < 2. The angles are complementary. The angles are complementary (So they add to 90 m< 1 + m < 2 = 90 3x + 7 + 7x + 3 = 90 10x + 10 = 90 1 2 10x = 80 x= 8 m<1= 3x + 7 m < 2 =7x + 3 m<1= 3(8) + 7 m< 2 = 7(8) + 3 m< 1 = 31 m < 2 =59 check: 31 + 59 = 90 which are complementary

  6. Supplementary Angles Supplementary Angles—two angles whose measures have the sum is 180 1 2 110 70 Adjacent and Non-adjacent and Supplementary supplementary m<1 + m < 2 = 180 110 = 180

  7. Example—Supplementary Angles Given m< 2 = 125Find the m< 1: This is a linear pair So the angles are supplementary (which means they add to 1802 1 m< 1 + m< 2 = 180 x + 125 = 180 x = 55 So m<1 = 55

  8. Complements and Supplements If you have an angle X It’s complement can be found by subtracting from 90 or (90 – x) It’s supplement can be found by subtracting from 180 or (180 - x)

  9. Example—Supplements and Complements Given: m <A = 72and m <B = (4x – 12) Find the complement and supplement of <A. Complement: 90 – 72 = 18 (or 72 + x = 90) Supplement: 180 – 72 = 108 (or 72 + x = 180) Find the complement and supplement of <B. Complement: 90– (4x -12) 90 – 4x + 12 (102 – 4x) Supplement: 180 – (4x -12) 180 – 4x + 12 (192 – 4x)

  10. VerticalAngles Vertical angles—two angles whose sides form two pairs of opposite rays 13 24 Picture always looks like an X < 1 and < 4 are vertical angles < 2 and < 3 are vertical angles

  11. Example—Identifying angle pairs Name a pair of each of the following angles: E F Complementary angles: D <ADB and <BDC A B C Supplementary angles: <ADE and <EDF Vertical angles: <EDA and <FDC

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