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1.4 – Measure and Classify Angles & Angle Constructions

1.4 – Measure and Classify Angles & Angle Constructions. 1.5 –Describe Angle Pair Relationships. B. 1. A. C. Two different rays with the same initial point. Measured in degrees. Angle:.  A ,.  BAC ,.  CAB,. 1. B. A. C. B. A. C. Common initial point, where rays meet.

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1.4 – Measure and Classify Angles & Angle Constructions

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  1. 1.4 – Measure and Classify Angles & Angle Constructions 1.5 –Describe Angle Pair Relationships

  2. B 1 A C Two different rays with the same initial point. Measured in degrees. Angle: A, BAC, CAB, 1

  3. B A C B A C Common initial point, where rays meet pt. A vertex side The rays of the angle side

  4. A Angle more than 0°, but less than 90° mA = 50° Angle that measures 90° mR = 90° R Angle more than 90°, but less than 180° mO = 110° O Angle that measures 180° mS = 180° S

  5. QS bisects PQR Ray that cuts an angle in half to make 2 congruent angles P S PQS SQR Q R

  6. Two angles that share a common side and vertex 1 is adjacent to 2 2 1

  7. Complementary Angles: Two angles that add to 90° 1 1 2 2 m1 + m2 = 90°

  8. Supplementary Angles: Two angles that add to 180° 1 2 1 2 m1 + m2 = 180°

  9. Supplementary angles that are adjacent Linear Pair: 2 1 m1 + m2 = 180°

  10. Vertical Angles: Two angles whose sides form two pairs of opposite rays 1 2 They will always be congruent!

  11. Angle Addition Postulate: If you add two adjacent angles, it totals to get their sum. C A B D mABC + mCBD = mABD

  12. 1. Give three names for the angle shown, then name the vertex and sides. DEF Pt. E FED E

  13. 1. Give three names for the angle shown, then name the vertex and sides. QVS Pt. V SVQ V

  14. 2. Classify the angle as acute, right, obtuse or straight. mA = 115° obtuse

  15. 2. Classify the angle as acute, right, obtuse or straight. mA = 90° right

  16. 2. Classify the angle as acute, right, obtuse or straight. mA = 85° acute

  17. 2. Classify the angle as acute, right, obtuse or straight. mA = 180° straight

  18. 3. Use a protractor to find the measure of the angle to the nearest degree. Then classify the angle as acute, obtuse, straight, or right. obtuse 91°

  19. 3. Use a protractor to find the measure of the angle to the nearest degree. Then classify the angle as acute, obtuse, straight, or right. acute 32°

  20. 3. Use a protractor to find the measure of the angle to the nearest degree. Then classify the angle as acute, obtuse, straight, or right. straight 180°

  21. 4. Find the indicated measure. mPRS = 81+42 mPRS = 123°

  22. 4. Find the indicated measure. mWXZ = 90 – 26 = mWXZ = 64°

  23. 5. Find each indicated angle. 15° 90° 90° 75° 15°

  24. 5. Find each indicated angle. 160° 20° 15° c = 180-90-75 = 15° a = 180-160 = 20° d = 180-90-15 = 75° b = 180-20 = 160°

  25. mNRP + mPRQ = mNRQ 8x + 7 + 4x – 1 = 78 12x + 6 = 78 12x = 72 x = 6 mPRQ = 4(6) – 1 mPRQ = 24 – 1 mPRQ = 23°

  26. mADB + mBDC = mADC 11x – 7 + 5x – 3 = 118 16x – 10 = 118 16x = 128 x = 8 mADB = 11(8) – 7 mADB = 88 – 7 mADB = 81°

  27. 5x + 2 = 7x – 6 2 = 2x – 6 8 = 2x 4 = x mABC = 20+2 +28-6 = 44° 5(4)+2 + 7(4)-6 =

  28. 5x + 13 = 9x – 23 13 = 4x – 23 36 = 4x 9 = x mABC = 45+13+81-23 = 116° 5(9)+13 + 9(9)-23 =

  29. 8. Tell whether the indicated angles are adjacent. EFG and HGF no

  30. 8. Tell whether the indicated angles are adjacent. JNM and MNK yes

  31. 9. Name a pair of complementary angles, supplementary angles, and vertical angles . Vertical: ROL and NOP L LOM and QOP M Complementary: R N QOR and ROL O MON and NOP Q P Supplementary: ROL and LON ROM and MON QOL and LOM

  32. 9. Name a pair of complementary angles, supplementary angles, and vertical angles . Vertical: DGE and BGC A EGB and DGC E Complementary: DGE and EGA G B D Supplementary: C DGE and EGB DGA and AGB EGA and AGC

  33. 10. 1 and 2 are complementary angles. Given the measure of 1, find m2. m1 = 82° m2 = 90 – 82 = 8°

  34. 10. 1 and 2 are complementary angles. Given the measure of 1, find m2. m1 = 23° m2 = 90 – 23 = 67°

  35. 11. 1 and 2 are supplementary angles. Given the measure of 1, find m2. m1 = 82° m2 = 180 – 82 = 98°

  36. 11. 1 and 2 are supplementary angles. Given the measure of 1, find m2. m1 = 105° m2 = 180 – 105 = 75°

  37. 12. Find the measure of ABD and DBC. 4x + 6 + 11x – 6 = 180 15x = 180 x = 12 4(12)+6 mABD = = 48+6 = 54° 11(12)-6 mDBC = = 132-6 = 126°

  38. 12. Find the measure of ABD and DBC. 2x + 3x = 90 5x = 90 x = 18 2(18) mABD = = 36° 3(18) mDBC = = 54°

  39. 13. Use the diagram below. Tell whether the angles are vertical angles, linear pair, or neither. 1 and 2 Linear pair

  40. 13. Use the diagram below. Tell whether the angles are vertical angles, linear pair, or neither. 2 and 4 Vertical angles

  41. 6. Use the diagram below. Tell whether the angles are vertical angles, linear pair, or neither. 5 and 8 neither

  42. 7. Find the values of x and y. 6x – 11 + 2x – 9 = 180 8x – 20 = 180 8x = 200 x = 25° 20y + 19 + 2x – 9 = 180 20y + 19 + 2(25) – 9 = 180 20y + 60 = 180 20y = 120 y = 6°

  43. 7. Find the values of x and y. 9x + 2 + 10x + 7 = 180 19x + 9 = 180 19x = 171 x = 9° 18y + 25 + 9x + 2 = 180 18y + 25 + 9(9) + 2 = 180 18y + 108 = 180 18y = 72 y = 4°

  44. HW Problem 1.4 # 38 53° 37° **Bring compass and ruler tomorrow! Books will not be needed

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