pairs of angles · angles pairs with special totals: 1. complementary angles sum to be 90°. 2....
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Pairs of Angles
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1. to identify adjacent, vertical, complementary, and supplementary angles
2. to find measures of pairs of angles
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two coplanar angles with a common side, a common vertex, and no common interior points.
1 2
3 4
∠1 and ∠2 are adjacent angles.
∠3 and ∠4 are adjacent angles.
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two nonadjacent angles formed by two intersecting lines
Vertical angle pairs: ∠1 𝑎𝑛𝑑 ∠3∠2 𝑎𝑛𝑑 ∠4
142
3
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two angles whose measures have a sum of 90˚. Each angle is called the complement of the other.
B
A
37˚
53˚
∠𝐴 𝑎𝑛𝑑 ∠𝐵 are a pair of complementary angles.
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two angles whose measures have a sum of 180˚. Each angle is called the supplement of the other.
CA
53˚ 127˚
∠𝐴 𝑎𝑛𝑑 ∠𝐶 are a pair of supplementary angles
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pair of adjacent angles whose non-common sides are opposite rays. The angles of a linear pair form a straight angle.
4 3
∠3 𝑎𝑛𝑑 ∠4 form a linear pair.
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Relationships you can assume true without marks:
Relationships that must be marked:
Angles are adjacent.
Angles are adjacent supplementary (form a line).
Angles are vertical angles.
Angles or segments are congruent.
An angle is a right angle.
Angles are complementary.
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Angles pairs with special totals:
1. Complementary angles sum to be 90°.
2. Supplementary angles sum to be 180°.
Angle pairs formed by intersecting lines.
3. Linear pairs are adjacent angles that are supplementary.
4. Vertical angles are opposite angles that are congruent.
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Find the measure of each angle in the angle pair described.
1. The measure of one angle is 5 times the measure of its complement.
2. ∠𝐴𝐵𝐶 and ∠𝐶𝐵𝐷 are supplementary. If 𝑚∠𝐴𝐵𝐶 = 4𝑥 + 73, and 𝑚∠𝐶𝐵𝐷 = 7𝑥 − 25, find the measures of both angles.
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Find the measure of each angle in the angle pair described.
1. The measure of one angle is 5 times the measure of its complement.
2. ∠𝐴𝐵𝐶 and ∠𝐶𝐵𝐷 are supplementary. If 𝑚∠𝐴𝐵𝐶 = 4𝑥 + 73, and 𝑚∠𝐶𝐵𝐷 = 7𝑥 − 25, find the measures of both angles.
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In the diagram at the right, mHKI = 48. Find each of the following.
mIKJ
mFKG
mFKH
mFKJ
mGKI
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In the diagram at the right, mHKI = 48. Find each of the following.
mIKJ
mFKG
mFKH
mFKJ
mGKI
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Got It: Represents and applies angle pairs to complex/real world situations
Almost There: Represent/apply angle pair properties with expressions
Moving Forward: Represent/apply angle pair properties without expressions.
Getting Started: Identifies angle pairs
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Pages 32 – 33
14 – 32 even
36, 40, 42