Download 1.5 angle relationships ink.notebook

1.5 angle relationships ink.notebook
August 30, 2016
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1.5 Angle
Relationships
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Lesson Objectives
Standards
Lesson Notes
1.5 Angle Relationships
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1.5 angle relationships ink.notebook
Lesson Objectives
Standards
August 30, 2016
Lesson Notes
Lesson Objectives
After this lesson, you should be able to successfully solve multi­step problems using angle relationships.
Standards
Lesson Notes
G.CO.1 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.
G.MG.1 Use geometric shapes, their measures, and their properties to describe objects.
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Complementary Angles
W
Y
65¡ 25¡ X
Z
ÛWXY is _________________ to ÛYXZ. Two ________ whose measures have a ______ of ______. Example: 30¡ x
x + 30 = 90
x = 60
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1.5 angle relationships ink.notebook
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Supplementary Angles
ÛHIJ is _________________ to ÛJIK. J
120¡ 60¡ Two ________ whose measures have a I
K ______ of ______. H
P
Example: x + 2 135¡ M
B
75¡ 105¡ C
A
D
N
x + 137 = 180
T
x = 43
Adjacent Angles
ÛACB and ÛACD are ________________. Two ________ that are ______ by ______. E
Have a common ________ and ______. W
Y
25¡ 25¡ X
Z
May or may not by ____________ depends if ___________. 3
1.5 angle relationships ink.notebook
August 30, 2016
Vertical Angles
ÛLMN & ÛOMP and ÛLMO & ÛNMP N
are ______________________. 40¡ 140¡ M 140¡ Two ________ formed by two _____________ lines. O 40¡ P
Always _______________. L
Another name is __________________.
Example: These angles are vertical. 2y + 30 2y + 30 = 3y ­ 85
2x + 1 = 65
65¡ 2x + 1
3y ­ 85 y = 115 x = 32
2 different ways to be supplementary
150¡
30¡
150¡
30¡
Linear Pair
A pair of adjacent angles with noncommon sides that are opposite rays is called a _________ _____.
150¡
30¡
They are supplementary
angles that are adjacent
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Name an angle or angle pair that satisfies each condition.
1. two adjacent angles
L
2. two acute vertical angles
3. two complementary angles
R 110¡ T
S
N
E
4. two supplementary adjacent angles
5. an angle supplementary to ÛRTS
Use the figure at the right for exercises 6 – 8.
6. Identify two vertical angles.
7. Identify two acute adjacent angles.
8. Identify an angle supplementary to ÛTNU.
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9. Find the measure of two complementary angles if the difference in their measures is 18.
10.
6. Find the value of y. 11.
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1.5 angle relationships ink.notebook
12.
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13.
E
Equation ___________________
8x 4x + 12 C
D
F
x = __________
mÛCDE = ________ mÛEDF _______
14. The basketball pole forms a pair of supplementary angles with the ground. Find m∠BCA and m∠DCA. (3x + 8)¡ (4x ­ 3)¡
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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.
16. Given that Û1 is a complement of Û2 and mÛ2 = 57°, find mÛ1. 17. Given that Û3 is a supplement of Û4 and mÛ4 = 41°, find mÛ3. 18. A sign painter is painting a large "X". What are the measures of angles 1, 2, and 3?
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1.5 angle relationships ink.notebook
On the
worksheet
For Exercises 1­6, use the figure at the right. Name an angle or angle pair that satisfies each condition.
1. Name two acute vertical angles.
August 30, 2016
Practice
7. Find the measures of an angle and its complement if one angle measures 24 degrees more than the other.
2. Name two obtuse vertical angles.
3. Name a linear pair.
4. Name two acute adjacent angles. 5. Name an angle complementary to ÛEKH.
6. Name an angle supplementary to ÛFKG.
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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. If mÛPTQ = 3y − 10 and mÛQTR = y, find the value of y so that ÛPTR is a right angle.
Determine whether each statement can be assumed from the figure. Explain.
11. ÛWZU is a right angle.
12. ÛYZU and ÛUZV are supplementary.
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1.5 angle relationships ink.notebook
Determine whether each statement can be assumed from the figure. Explain.
13. ÛVZU is adjacent to ÛYZX. August 30, 2016
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?
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17. If mÛBGC = 16x − 4 and mÛCGD = 2x + 13, find the value of x so that ÛBGD is a right angle
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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.
a. Find the measure of Û1.
b. Find the measure of Û4.
135¡ 1 3 2 50 ¡
4 c. Name a pair of vertical angles in the figure. d. What is the measure of Û2? Answers:
1. ÛEKH and ÛFKG 3. ÛEKF and ÛHKG 5. ÛGKJ
7. 2x + 24 = 90, 33 and 57 9. 8x + 18 = 90, x = 9 11. Yes it is marked with a rt Û symbol 13. No the Û’s do not share a common side 15. 2x – 78 = 180, 23 and 67 17. 18x + 9 = 90, x = 4.5 12