Download Section 1.6 Angle Pair Relationships

Section 1.6
Angle Pair Relationships
standard #13
5/3/2017
Goals
• Vertical Angles and
Linear Pairs
• Complementary and
Supplementary Angles
Vertical Angles
2 angles whose sides form two pairs of
opposite rays. These angles are congruent
and lie on opposite sides of the point of
intersection.
<1 & <2 are vertical.
m<1 ≅ m< 2.
3
1
2
4
<3 & <4 are vertical.
m<3 ≅ m<4.
Linear Pair
• Two adjacent angles whose non-common
sides are opposite rays. The angles will add
up to 180°. The angles lie on the same line.
1
2
m<1 + m<2 = 180°
Complementary Angles
• Two angles that add to 90°. Each angle is the
complement of the other. However, these angles
do not have to be adjacent in order to be
complementary.
1
2
m<1 + m<2 = 90°
Supplementary Angles
• Two angles that add to 180°. Each angle is the
supplement of the other. However, these angles
do not have to be adjacent in order to be
supplementary.
m<1 + m<2 = 180°
1
2
Example #1
A. Are 1 and 2 a linear pair? Yes
B. Are 4 and 5 a linear pair? No,
No, <3≠<5
C. Are 5 and 3 vertical angles?<4+<5≠180°
D. Are 1 and 3 vertical angles? Yes
2
3
1
5
4
Example #2
• In one town, Main Street and Columbus
Avenue intersect to form an angle of 36°.
Find the measures of the other three
angles.
1
36
2
3
Answers to #2
1) m<1 = 144°
2) m<2 = 36°
(180-36)
(Vertical Angles are congruent)
3) m<3 = 144°
(Vertical Angles are congruent)
1
36
°
2
3
Example #3
Solve for x and y. Then find the angle measures.
4x+15
5x+30
3y+15
3y-15
Answers to #3
1)
2)
3)
4)
X
4x + 15 + 5x + 30 = 180°
9x + 45 = 180°
9x = 135°
x = 15
Y
1)
2)
3)
3y + 15 + 3y - 15 =
180°
6y = 180°
y = 30
Example #4
A. Given that G is a supplement of H and
mG is 82°, find mH.
B. Given that U is a complement of V, and
mU is 73°, find mV.
Answers to #4
1) 82° + mH = 180°
2) mH = 98°
1) 73° + mV = 90°
2) mV = 17°
Assignment
Page 47
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