chapter 1-5 notes - mr. burdick's math...
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Chapter 1-5 Notes
Definitions
• Complementary
• When two angles add up to
• Do not have to be
• Do not have to be
90
congruent
next to each other
Examples
• Example 1
The two angles below are complementary. What is the value of x?
34 + x = 90
– 34 – 34
x = 56
Examples
• Example 2
A and B are complementary. mA = 21. What is mB?
mA + mB = 90
21 + mB = 90
– 21 – 21
mB = 69
Examples
• Example 3
The two angles below are complimentary. Find the measure of each angle.
mLKJ + mIHG = 90
7r + 5 + 8r + 9 = 90
15r + 14 = 90– 14 – 14
15r = 76𝟏𝟓 𝟏𝟓
r = 5.1
Example 3 continued
mIHG = 8r + 9 mLKJ = 7r + 5
mIHG = 8(5.1) + 9
mIHG = 40.8 + 9
mIHG = 49.8
mLKJ = 7(5.7) + 5
mIHG = 35.7 + 5
mIHG = 40.7
Examples
• Example 4
A and B are complementary. mA = 4x – 4 and mB = 2x + 28. Find the measure of each angle.
mA + mB = 90
4x – 4 + 2x + 28 = 90
6x + 24 = 90
– 24 – 246x = 66 𝟔 𝟔x = 11
mA = 4x – 4 mB = 2x + 28
mA = 4(11) – 4
mA = 44 – 4
mA = 40
mB = 2(11) + 28
mB = 22 + 28
mB = 50
Definitions
• Supplementary
• When two angles add up to
• Do not have to be
• Do not have to be
180
congruent
next to each other
Examples
• Example 5
The two angles below are supplementary. If mMNO = 78, what is mPQR?
mMNO + mPQR = 180
78+ mPQR = 180
– 78 – 78
mPQR = 102
Examples
• Example 6
A and B are supplementary. mB = 99. What is mA?
mA + mB = 180
mA + 99 = 180
– 99 – 99
mA = 81
Examples
• Example 7
What is the measure of two congruent, supplementary angles?
mA + mB = 180 mA = mB
mA + mA = 180
2*mA = 180 𝟐 𝟐
mA = 90 mB = 90
Definitions
• Adjacent Angles
• Two angles that have the same , share a , and do not
• Linear Pair
• Two angles that are and whose non-common sides form a
• Linear Pair angles are
vertex side overlap
adjacent straight line
supplementary
Examples
• Example 8
What is the value of each angle?
mABD + mCBD = 180
7q – 46 + 3q + 6 = 18010q – 40 = 180
+ 40 + 4010q = 220𝟏𝟎 𝟏𝟎
q = 22
Example 8 continued
mABD = 7q – 46 mCBD = 3q + 6
mABD = 7(22) – 46
mABD = 154 – 46
mABD = 108
mCBD = 3(22) + 6
mCBD = 66 + 6
mCBD = 72
Definitions
• Vertical Angles
• Two non-adjacent angles formed by intersecting lines
Theorems
• Vertical Angles Theorem
• If two angles are vertical angles, then they are congruent
Examples
• Example 9
Find m1 and m2.
m1 = 18
m1 + m2 = 180
18 + m2 = 180– 18 – 18
m2 = 162