Angles. Problems: A.! Name the vertex of the angle. What rays are the sides of the angle? C.! Give three other names of LJK.

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1 ngles page # Problems:. ngles. Name the vertex of the angle.. What rays are the sides of the angle? J. Give three other names of LJK.. Name the following angles with three letters: = = N M The remaining angle: O L Protractor work: 3. Measure the following angles with a protractor:....

2 ngles page # 4. raw angles with the measures given: Measure angles through G =. E F G + E + F + G =

3 ngles page #3 6. raw:. an acute angle:. a right angle:. an obtuse angle:. a straight angle: djacent ngles: 7. E. Name 4 different pairs of adjacent angles. and and and and. Name two different acute angles. and. Name one obtuse angle.. Name two different right angles. and

4 ngles page #4 8. Perpendicular Lines: raw two lines that are perpendicular: 9. omplementary angles: raw two angles that are complementary: 0. Supplementary angles: raw two angles that are supplementary:. ngles of a Linear Pair: raw two angles that form a linear pair Problems: = 3 3. If E, find m. (0.6x+34) 50 ( 3 x+30 ) E

5 ngles page #5 4. E. Name different pairs of supplementary angles. and and. If is perpendicular to E:. Name two different right angles. and. Name a pair of complementary angles. and 5. Given: m = 3(x + y) m = 6(x y) Solve for y in terms of x. 6. The measure of an angle is 8 times the measure of its supplement. Find the measure of each angle

6 ngles page #6 7. The measure of an angle is 5 times the measure of its supplement. Find the measure of each angle. 8. The measure of an angle is times the measure of its complement. find the measure of each angle. 9. The measure of an angle is 5 more than 4 times the measure of its supplement. find the measure of each angle. 0. The measure of an angle is 4 more than the measure of its complement. Find the measure of each angle.

7 ngles page #7. The measure of an angle is 0 less than 4 times the measure of its supplement. Find the measure of each angle.. Two angles are equal and complementary. What is the measure of each? 3. Given: PO O, PO is six times as large as O P O Solve for x and find the measure of each acute angle. 4. is acute. m = x 0 5. O is obtuse. m O = 4x + 64 a. What are the restrictions on m? a. What are the restrictions on m O? b. What are the restrictions on x? b. What are the restrictions on x?

8 ngles page #8 6. Given: ETR is a straight angle Given: and have the m ETS = x same measure. m STR = 7 x m = x + 60 Is STR a right angle? Justify m = x 35 Is a straight angle? Justify S E T R 8. Given: is a right angle. = ( 0x + 7) o = ( 5x + 8) o Find the value of x, m, and m.

9 ngles page #9 9. Use your protractor to draw the following:. Two adjacent complementary angles, one that has the measure 4.. Two adjacent supplementary angles, one that has the measure Write a formula (equation) for and :. If = x+3 and = x-6, then: x = = =. If = 3x-4 and = x+9, then: x = = =

10 ngles page # If = 37 and = 45 then 3 =. if + 3 = 08, then = 3.. Write a formula (equation) for and :. If = 3x + 6 and = 4x, then: x = = =. If = x 4 and = x, then: x = = =

11 ngles page # 33. Find the measure of each numbered angle = = 3 = 4 = 5 = lgebra Skills 34. Solve for y in terms of x: 3x 5y = Solve for x in terms of y: x + 6y = 36. Factor: a. x 49 b. x 3x 54 c. x 7x Solve for x: a. x + 6x + 8 = 0 b. x 7x = 8 c. 5x + x 0 = x + 6x 3

12 ngles page # 38.(ST Problem) 39.Solve for x and find m : Solve for y: 50 (y 40) (x +3x) (0x+40) 40. Solve for x and find m : 4. Solve for x and find m : (x +x+) (x x+49) (3x +0x+00) (3x +3x+76) 4. Solve for y in terms of x: 43. Given that, solve for x: S (x+y) (3x 8) (x 54) P Q R

13 ngles page #3 Vertical ngles Problems:. Z V U Y W X. and form a vertical pair.. o and 3 form a vertical pair?. o and 4 form a vertical pair?. What angle forms a vertical pair with?. Find the measures of angles through = = 5 = 3 = 6 = 4 = 7 =

14 ngles page #4 3. Find x and the measure of each angle:. 8x 0x-30. x+45 x. 6x 0x-3. 3x x+8

15 ngles page # Name two pairs of vertical angles: and E and. The angle vertical to E is.. Name 4 pairs of supplementary angles: and and and and. If E = 4, then: = = = 5. Find x and the measure of each angle.... 3x+0 5x 5x x 4x 5x-7 8. Given: m = 3x + y + 5 m = 0y 4x m 3 = x + y Find: m, m, m 3 3

16 ngles page #6 9. Given: = (0 x)o = (7 x) o = (x + ) o = ( 5x) o Show that Find all possible values of x, and (0 x) (x ) E Solve for x and y: (y-5) (3x) (x) (y)

17 ngles page #7 5. Find all possible values for x and the measure of all 4 angles in diagram ( 3x +5x+5) ( x +6x+5) 5. (ST Problem) Three lines intersect as shown. What is the value of x + y? y x 30 Proving that Vertical ngles are Equal theorem is a statement that you can prove. Theorem: Vertical ngles are equal. 3 4 Prove: = and 3 = 4

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