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1.4 – Measure and Classify Angles & Angle Constructions 1.5 –Describe Angle Pair Relationships Angle: Two different rays with the same initial point. Measured in degrees. B A 1 C A, BAC, CAB, 1 B Common initial A Vertex point, where rays meet C pt. A vertex side Sides The rays of the angle B A AB C side AC Acute Right Angle more than 0°, but less than 90° Angle that measures 90° Obtuse Angle more than 90°, but less than 180° Straight Angle that measures 180° mA = 50° A mR = 90° R mO = 110° O S mS = 180° Ray that cuts an P angle in Angle half to Bisector make 2 congruent Q angles QS bisects PQR S R PQS SQR Two angles Adjacent that share angles a common side and vertex 2 1 1 is adjacent to 2 Complementary Angles: Two angles that add to 90° 1 1 2 m1 + m2 = 90° 2 Supplementary Angles: Two angles that add to 180° 1 1 2 2 m1 + m2 = 180° Linear Pair: Supplementary angles that are adjacent 1 2 m1 + m2 = 180° Vertical Angles: Two angles whose sides form two pairs of opposite rays 1 2 They will always be congruent! 1 2 Angle Addition Postulate: If you add two adjacent angles, it totals to get their sum. C A B D mABC + mCBD = mABD 1. Give three names for the angle shown, then name the vertex and sides. Names Vertex DEF FED E Pt. E Sides ED EF 1. Give three names for the angle shown, then name the vertex and sides. Names QVS SVQ V Vertex Pt. V Sides VQ VS 2. Classify the angle as acute, right, obtuse or straight. mA = 115° obtuse 2. Classify the angle as acute, right, obtuse or straight. mA = 90° right 2. Classify the angle as acute, right, obtuse or straight. mA = 85° acute 2. Classify the angle as acute, right, obtuse or straight. mA = 180° straight 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. 91° obtuse 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. 32° acute 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. 180° straight 4. Find the indicated measure. mPRS = 81+42 mPRS = 123° 4. Find the indicated measure. mWXZ = 90 – 26 = mWXZ = 64° 5. Find each indicated angle. 15° 90° 90° 75° 15° 5. Find each indicated angle. 20° 15° a = 180-160 = 20° b = 180-20 = 160° 160° c = 180-90-75 = 15° d = 180-90-15 = 75° mNRP + mPRQ = mNRQ 8x + 7 + 4x – 1 = 78 12x + 6 = 78 12x = 72 x=6 mPRQ = 4(6) – 1 mPRQ = 24 – 1 mPRQ = 23° mADB + mBDC = mADC 11x – 7 + 5x – 3 = 118 16x – 10 = 118 16x = 128 x=8 mADB = 11(8) – 7 mADB = 88 – 7 mADB = 81° 5x + 2 = 7x – 6 2 = 2x – 6 8 = 2x 4=x mABC = 5(4)+2 + 7(4)-6 = 20+2 +28-6 = 44° 5x + 13 = 9x – 23 13 = 4x – 23 36 = 4x 9=x mABC = 5(9)+13 + 9(9)-23 = 45+13+81-23 = 116° 8. Tell whether the indicated angles are adjacent. EFG and HGF no 8. Tell whether the indicated angles are adjacent. JNM and MNK yes 9. Name a pair of complementary angles, supplementary angles, and vertical angles . Vertical: ROL and NOP L M R N O Q P LOM and QOP Complementary: QOR and ROL MON and NOP Supplementary: ROL and LON ROM and MON QOL and LOM 9. Name a pair of complementary angles, supplementary angles, and vertical angles . Vertical: DGE and BGC A EGB and DGC E D G B C Complementary: DGE and EGA Supplementary: DGE and EGB DGA and AGB EGA and AGC 10. 1 and 2 are complementary angles. Given the measure of 1, find m2. m1 = 82° m2 = 90 – 82 = 8° 10. 1 and 2 are complementary angles. Given the measure of 1, find m2. m1 = 23° m2 = 90 – 23 = 67° 11. 1 and 2 are supplementary angles. Given the measure of 1, find m2. m1 = 82° m2 = 180 – 82 = 98° 11. 1 and 2 are supplementary angles. Given the measure of 1, find m2. m1 = 105° m2 = 180 – 105 = 75° 12. Find the measure of ABD and DBC. 4x + 6 + 11x – 6 = 180 15x = 180 x = 12 mABD = 4(12)+6 = 48+6 = 54° mDBC = 11(12)-6 = 132-6 = 126° 12. Find the measure of ABD and DBC. 2x + 3x = 90 5x = 90 x = 18 mABD = 2(18) = 36° mDBC = 3(18) = 54° 13. Use the diagram below. Tell whether the angles are vertical angles, linear pair, or neither. 1 and 2 Linear pair 13. Use the diagram below. Tell whether the angles are vertical angles, linear pair, or neither. 2 and 4 Vertical angles 6. Use the diagram below. Tell whether the angles are vertical angles, linear pair, or neither. 5 and 8 neither 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° 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° HW Problem 1.4 1.5 28-32 4-18 even, 21, 22, 24-27, 33-38 (draw pic), 40, 41 38-41 4, 5, 7-33 odd, 49-52, 61, 62 1.4 # 38 53° 37° **Bring compass and ruler tomorrow! Books will not be needed