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! ! ! ! ! ! Angles ! ! ! ! Angles Problems: 1. J ! 2. ! A. ! Name the vertex of the angle. B.! What rays are the sides of the angle? C.! Give three other names of !LJK . ! ! ! ! Name the following angles with three letters: "1 = __________ M N " 2 = __________ 1 ! ! 2 The remaining angle: __________ O Protractor work: 3. Measure the following angles with a protractor: A.! ! ! ! ! ! ! B. C.! ! ! ! ! ! ! D. L ! page #1 ! ! ! ! ! ! Angles ! ! ! ! 4. Draw angles with the measures given: ! A. 42°! ! ! ! ! ! B. 133° 5. Measure angles A through G. A. A B C " A + "B + " C = _____________________________ ! B. ! F E G D ! ! " D + " E + " F + " G = ____________________________ ! ! ! ! page #2 ! ! ! ! ! ! Angles ! ! ! ! ! 6. Draw: A. an acute angle: B. a right angle: C. an obtuse angle: D. a straight angle: Adjacent Angles: 7. C D ! ! A. Name 4 different pairs of adjacent angles. ! ! __________ and __________ ! ! __________ and __________ ! ! __________ and __________ ! ! __________ and __________ ! B. Name two different acute angles. __________ and __________ ! C. Name one obtuse angle. __________ ! D. Name two different right angles. __________ and __________ A B E page #3 ! ! ! ! ! ! Angles ! ! ! ! ! page #4 8. Perpendicular Lines: Draw two lines that are perpendicular: 9. Complementary angles: Draw two angles that are complementary: 10. Supplementary angles: Draw two angles that are supplementary: 11. Angles of a Linear Pair: Draw two angles that form a linear pair Problems: 12. "1 + "2 + "3 = _________________ 2 1 ! 3 ! 13.! If !CBD " !DBE , find m!A . D C 50° (0.6x+34)° A B ( 1 3 ) x+30 ° E ! ! ! ! ! ! ! ! Angles ! ! ! ! ! page #5 14. C D ! ! ! A. Name 2 different pairs of supplementary angles. ! ! __________ and __________ ! ! __________ and __________ ! B. If CB is perpendicular to AE: ! ! 1. Name two different right angles. __________ and __________ ! ! 2. Name a pair of complementary angles. _________ and __________ A 15. Given:! ! ! ! ! B E !1" !2 m"1 = 3(x + 2y) m"2 = 6(x # y) Solve for y in terms of x. ! 16. ! The measure of an angle is 8 times the measure of its supplement. Find the measure ! of each angle ! ! ! ! ! ! Angles ! ! ! ! ! page #6 17. ! The measure of an angle is 5 times the measure of its supplement. Find the measure ! of each angle. 18. ! The measure of an angle is 2 times the measure of its complement. find the measure ! of each angle. 19. ! The measure of an angle is 5 more than 4 times the measure of its supplement. find ! the measure of each angle. 20. ! The measure of an angle is 24 more than the measure of its complement. Find the ! measure of each angle. ! ! ! ! ! ! Angles ! ! ! ! ! page #7 21. The measure of an angle is 20 less than 4 times the measure of its supplement. Find ! the measure of each angle. 22. Two angles are equal and complementary. What is the measure of each? 23. Given: PO ! OA , !POC is six times as large as !COA P C O A Solve for x and find the measure of each acute angle.! ! 24.! !A is acute. m!A = 2x " 20 ! ! ! a.! What are the restrictions on m!A ?! b.! What are the restrictions on x ?! 25.! !O is obtuse. m!O = 4x + 64 a.! What are the restrictions on m!O ? b.! What are the restrictions on x ? ! ! 26. ! ! ! ! Given:! !ETR is a straight angle.! 9.! ! m!ETS = 148 + 7x ! ! m!STR = 72 " 2x ! ! Angles ! 27. ! ! ! page #8 Given:!!ABC and !CBD have the same measure. 1 x + 60 2 m!CBD = 2x " 35 m!ABC = Is !STR a right angle? Justify!! ! Is !ABD a straight angle? Justify! C S E T A R ! ! ! ! A 28. Given:! !ABC is a right angle. D ! ! !ABD = (120x + 27 ) ! !CBD = (15x + 18 ) ! ! ! B Find the value of x, m!ABD , and m!CBD . C B D ! ! ! ! ! ! Angles ! ! ! ! ! page #9 29. Use your protractor to draw the following: ! A. Two adjacent complementary angles, one that has the measure 42°. ! B. Two adjacent supplementary angles, one that has the measure 42°. 30. ! ! ! ! ! 1 ! 2 A. Write a formula (equation) for "1 and "2: ___________________________ B. If "1 = 2x+3 and "2 = x-6, then: ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! x = __________ ! "1 = __________ ! "2 = __________ ! x = __________ ! ! ! ! C. If "1 = 3x-4 and "2 = 2x+9, then:! ! ! ! ! ! ! ! ! ! ! ! !! ! ! ! ! ! "1 = __________ ! ! ! ! ! ! ! ! ! "2 = __________ ! ! ! ! ! ! ! Angles ! ! ! ! ! page #10 31. 2 1 ! ! 3 A. If "1 = 37° and "2 = 45° then "3 = __________ ! ! B. if "1 + "3 ! = 108°, then! "2 = __________ ! ! ! 32. ! 2 1 ! ! A. Write a formula (equation) for "1 and "2: ! ! B. If "1 = 3x + 6 and "2!= 4x, then: ! ! ! ! ! ! ! ! __________________________ ! x = __________ ! ! ! ! ! ! ! ! ! ! ! " 1 = __________ ! ! ! ! ! ! ! ! ! " 2 = __________ ! x = __________ ! ! ! ! C. If "1 = 2x – 4 and "2 = x – 2, then: ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! "1 = __________ ! ! ! ! ! ! ! ! ! "2 = __________ ! ! ! ! ! ! ! Angles ! ! ! ! ! page #11 33. Find the measure of each numbered angle. 48° 1 3 101° 2 4 "1 = __________ ! ! ! ! ! ! ! ! ! ! "2 = __________ ! ! ! ! ! ! 104° 5 "3 = __________ ! "4 = __________ ! "5 = __________ 35. ! Solve for x in terms of y: 2x + 6y = 21 ! ! ! ! ! ! Algebra Skills 34.! ! Solve for y in terms of x: 3x ! 5y = 20 36.! Factor: a. x 2 ! 49 ! ! ! ! b. x 2 ! 3x ! 54 ! ! ! c.! 37.! Solve for x: a. x 2 + 16x + 28 = 0 ! ! b. x 2 ! 7x = 18 ! ! ! c. 2x 2 ! 17x + 30 5x 2 + 2x ! 10 = 2x 2 + 6x ! 3 ! ! ! ! ! ! Angles ! 38.!(SAT Problem)! ! Solve for y: ! ! ! ! 39.!Solve for x and find m!ABC : C (x2+3x)° 50° (y – 40)° ! ! 40.! Solve for x and find m!ABC :! ! A B D 41.! Solve for x and find m!ABC : C C (2x2+x+121)° A ! (10x+40)° (3x2+20x+100)° (x2–2x+49)° B D 42.! Solve for y in terms of x:! A ! B S ! P Q (3x–8)° (x2–54)° R ! D 43.! Given that AB ! BC , solve for x: A (x+y)° (3x2+3x+76)° B C page #12
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