1.5 angle relationships ink.notebook. September 01, Page Angle Relationships. Page 42. Page 44. Page 45. Page 43.

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1 Page Angle Relationships Page 43 Page 44 Page 42 Page 45 Page 46 1

2 Lesson Objectives Standards Lesson Notes Lesson Objectives Standards Lesson Notes 1.5 Angle Relationships After this lesson, you should be able to successfully solve multi step problems using angle relationships. Press the tabs to view details. Press the tabs to view details. G.CO.1 Lesson Objectives Standards Lesson Notes Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. Complementary Angles W WXY is to YXZ. Y 65 X 25 Z Two whose measures have a of. G.MG.1 Use geometric shapes, their measures, and their properties to describe objects. Example: 30 x x + 30 = 90 x = 60 Press the tabs to view details. 2

3 Supplementary Angles ÛHIJ is to ÛJIK. J I H Two whose measures have a K of. P Example: x+2 M A B C D x = N T x = 43 Adjacent Angles ÛACB and ÛACD are. Two that are by. E Have a common and. W Y X Z May or may not be depends if. 3

4 Vertical Angles ÛLMN & ÛOMP and ÛLMO & ÛNMP N are M 140 Two formed by two lines. O 40 P Always. L Another name is. Example: These angles are vertical. 2y x + 1 = 65 2y + 30 = 3y 85 x = 32 y = x + 1 3y 85 2 different ways to be supplementary Linear Pair A pair of adjacent angles with noncommon sides that are opposite rays is called a They are supplementary angles that are adjacent 4

5 Name an angle or angle pair that satisfies each condition. 1. two adjacent angles L 2. two acute vertical angles N R two complementary angles T E S 4. two supplementary adjacent angles 5. an angle supplementary to ÛRTS Use the figure at the right for exercises Identify two vertical angles. 7. Identify two acute adjacent angles. 8. Identify an angle supplementary to ÛTNU. 5

6 9. Find the measure of two complementary angles if the difference in their measures is Find the value of y

7 E 8x C Equation 4x + 12 D F x = mûcde = mûedf 7

8 14. The basketball pole forms a pair of supplementary angles with the ground. Find m BCA and m DCA. 15. Two angles form a linear pair. The measure of one angle is 4 times the measure of the other. Find the measure of each angle. (3x + 8) (4x 3) 16. Given that 1 is a complement of 2 and m 2 = 57, find m Given that 3 is a supplement of 4 and m 4 = 41, find m A sign painter is painting a large "X". What are the measures of angles 1, 2, and 3? 8

9 adjacent complementary (= 90) vertical (=) Supplementary (= 180) On the worksheet 9

10 For Exercises 1 6, use the figure at the right. Name an angle or angle pair that satisfies each condition. 1. Name two acute vertical angles. 2. Name two obtuse vertical angles. Practice 3. Name a linear pair. 4. Name two acute adjacent angles. 5. Name an angle complementary to EKH. 6. Name an angle supplementary to FKG. 7. Find the measures of an angle and its complement if one angle measures 24 degrees more than the other. 8. The measure of the supplement of an angle is 36 less than the measure of the angle. Find the measures of the angles. 10

11 10. If m PTQ = 3y 10 and m QTR = y, find the value of y so that PTR is a right angle. Determine whether each statement can be assumed from the figure. Explain. 11. WZU is a right angle. Determine whether each statement can be assumed from the figure. Explain. 13. VZU is adjacent to YZX. 12. YZU and UZV are supplementary. 11

12 14. Two angles are complementary. The measure of one angle is 21 more than twice the measure of the other angle. Find the measures of the angles. 15. If a supplement of an angle has a measure 78 less than the measure of the angle, what are the measures of the angles? 17. If m BGC = 16x 4 and m CGD = 2x + 13, find the value of x so that BGD is a right angle 12

13 Answers: 18. A rectangular plaza has a walking path along its perimeter in addition to two paths that cut across the plaza as shown in the figure. 1. EKH and FKG 3. EKF and HKG 5. GKJ a. Find the measure of 1. b. Find the measure of 4. c. Name a pair of vertical angles in the figure x + 24 = 90, 33 and x + 18 = 90, x = Yes it is marked with a rt symbol 13. No the s do not share a common side 15. 2x 78 = 180, 23 and x + 9 = 90, x = 4.5 d. What is the measure of 2? 13