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Lets Talk Angles

Take the following notes in your journal or on notebook paper. You will need to refer to them in class tomorrow . Lets Talk Angles. Vocabulary. ANGLE CONGRUENT ANGLES RIGHT ANGLE LINEAR PAIR VERTEX OBTUSE ANGLE

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Lets Talk Angles

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  1. Take the following notes in your journal or on notebook paper. You will need to refer to them in class tomorrow  Lets Talk Angles

  2. Vocabulary ANGLE CONGRUENT ANGLES RIGHT ANGLE LINEAR PAIR VERTEXOBTUSE ANGLE INTERIOR OF AN ANGLE STRAIGHT ANGLE EXTERIOR OF AN ANGLE MEASURE ANGLE BISECTOR ADJACENT ANGLES COMPLEMENTARY ANGLES SUPPLEMENTARY ANGLES VERTICAL DEGREE ACUTE ANGLE

  3. Example 1 : Naming Angles A surveyor recorded the angles formed by a transit (point A) and three distant points, B, C, and D. Name three of the angles. Possible answer: BAC CAD BAD

  4. Congruent angles are angles that have the same measure. In the diagram, mABC = mDEF, so you can write ABC  DEF. This is read as “angle ABC is congruent to angle DEF.” Arc marks are used to show that the two angles are congruent. The Angle Addition Postulate is very similar to the Segment Addition Postulate that you learned in the previous lesson.

  5. –48°–48° Example 2: Using the Angle Addition Postulate mDEG = 115°, and mDEF = 48°. Find mFEG mDEG = mDEF + mFEG  Add. Post. 115= 48+ mFEG Substitute the given values. Subtract 48 from both sides. 67= mFEG Simplify.

  6. An angle bisector is a ray that divides an angle into two congruent angles. JK bisects LJM; thus LJKKJM.

  7. KM bisects JKL, mJKM = (4x + 6)°, and mMKL = (7x – 12)°. Find mJKM. Example 3: Finding the Measure of an Angle

  8. Example 4: Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent. 7 and 8 7and 8have a common vertex, P, but do not have a common side. So 7and 8are not adjacent angles.

  9. *You can find the complement of an angle that measures x° by subtracting its measure from 90°, or (90 – x)°. *You can find the supplement of an angle that measures x° by subtracting its measure from 180°, or (180 – x)°.

  10. Example 5: Finding the Measures of Complements and Supplements Find the measure of each of the following. A. complement of F (90– x) 90 –59=31 B. supplement of G (180– x) 180– (7x+10)= 180 – 7x– 10 = (170– 7x)

  11. Another angle pair relationship exists between two angles whose sides form two pairs of opposite rays. Vertical anglesare two nonadjacent angles formed by two intersecting lines. 1and 3are vertical angles, as are 2and 4.

  12. Example 6: Identifying Vertical Angles Name the pairs of vertical angles. HML and JMK are vertical angles. HMJ and LMK are vertical angles. Check mHML  mJMK  60°. mHMJ  mLMK  120°.

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