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4.1 NotesFill in your notes
Adjacent angles share a ______________ and _______, but have no _______________________.vertex side
Points in common
Complementary Angles – Two angles whose measures have a sum of _______. Complementary angles can be ___________ or _____________. If mA = 50 and mB = 40, then A and B are complementary. A is the ____________ of B. Supplementary Angles – Two angles whose measures have a sum of ______. Supplementary angles can be _____________ or _________________.
C and D are supplementary. D is the ______________ of C. If A and B are complementary and mA = 85, find mB. If C and D are supplementary and mC = 85, find mD.
90°adjacent
nonadjacent
complement
180°adjace
ntnonadjacent
supplement
mA + mB = 90° so 85 + mB = 90°mB = 5°
mC + mD = 180° so 85 + mD = 180°mD = 95°
s
s
s
Name a pair of…..
Complementary
Supplementary
Adjacent
FGK and GKL (add to 90°)
HGK and GKL (add to 180°)
FGK and HGK (share a side and vertex but no common interior points)
Example: and are complementary angles. Find the measure of the angles if and
LMN PQR
mLMN 4x 2 mPQR9x1
mLMN + mPQR = 90° (definition of complementary angles) 4x -2 + 9x +1 = 90° 13x -1 = 90° 13x = 91° x = 7
mLMN = 4x -2 = 4(7) -2 = 28 – 2 = 26° mPQR = 9x + 1 = 9(7) + 1 = 63 + 1 = 64°
Check: 64 + 26 = 90
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Linear Pair of angles – Two adjacent angles whose _________________sides form ______________.
Vertical Angles – Two angles whose sides form ________________________ OR a pair of ______________ angles formed by ________________________________.nonadjacent
Noncommon sides
Two intersecting lines
Opposite rays
2 pairs of opposite rays
Vertical Angle Congruence Theorem – Vertical angles are congruent.
Example – 1 and 3 are a linear pair. 1 and 4 are a linear pair. 1 and 2 are vertical angles.True or false?
432
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a) b) c)
d) e) f)
truefalse false
false true true
m1 + m2 + m3 + 78 = 180° (makes a straight line)m1 + 90 + 78 = 180° (since 2 and 3 are complementary, they add to 90)m1 + 168 = 180°m1 = 12° m1 = m3 = m4 = 12° m2 + m3 = 90° (since they are complementary)SO… m2 + 12 = 90° and m2 = 78°
yes
no
no
yes
2 and 3
2 and (5 + 4) are vertical angles
5 + 4 = 90 + 60 = 150 SO…. m 2 = 150°
1 = x and 2 = 3x
1 + 2 = 180° (definition of linear pair)
x + 3x = 180° (definition of linear pair)
4x = 180°
x = 45°
1 = x and 2 = 3x
1 = 45° and 2 = 135°
(4x+15) + (5x + 30) = 180° (makes a straight line)
X = 15
(3y + 15) + (3y - 15) = 180° (makes a straight line)
y = 30
105°
105°
75°
75°
coplanar
collinear
between
B
We don’t know
We don’t know
We don’t know