1. TODAY IN GEOMETRY…
Learning Goal: 1.5 Angle Pair Relationships-Adjacent Angles, Complementary Angles, Supplementary Angles, Linear Angles, Vertical Angles
Independent Practice – NO A.T.

2. ∠1 and ∠2 are adjacent angles.
ADJACENT ANGLES: Two angles that are beside each other. 1 2
Shared side
Shared vertex
∠1 and ∠2 are adjacent angles.

3. COMPLEMENTARY ANGLES: Two angles whose sum is 90°.
42°
48°
Any two adjacent angles that form a right angle are complementary angles.
Two non-adjacent angles whose sum is 90°, are complementary.

4. PRACTICE: Angles 1 and 2 are complementary. Angle 1 is 75°
PRACTICE: Angles 1 and 2 are complementary. Angle 1 is 75°. Find angle 2. 1 2
75°
𝟏𝟓°
Definition of Complementary Angles 𝑚∠1+𝑚∠2=90°
Substitute known values °+𝑚∠2=90°
Subtract − 75° − 75° 𝒎∠𝟐=𝟏𝟓°

5. 3 4 ∠3=4𝑥−2 ∠3=4 7 −2 ∠3=28−2 ∠𝟑=𝟐𝟔° ∠4=9𝑥+1 ∠4=9 7 +1 ∠4=63+1 ∠𝟒=𝟔𝟒°
PRACTICE: Angle 3 and 4 are complementary angles. Find the measure of angle 3 and 4 if ∠3=4𝑥−2 and ∠4=9𝑥+1. 3 4
∠3=4𝑥−2
∠3=4 7 −2
∠3=28−2
∠𝟑=𝟐𝟔°
∠4=9𝑥+1
∠4=9 7 +1
∠4=63+1
∠𝟒=𝟔𝟒°
Definition of Complementary Angles 𝑚∠3+𝑚∠4=90
Substitute known values 4𝑥−2 +(9𝑥+1)=90
Combine like terms 𝑥−1=90
Add
13𝑥=91
Divide
𝒙=𝟕

6. SUPPLEMENTARY ANGLES: Two angles whose sum is 180°.
Any two adjacent angles that form a straight angle are supplementary angles. 3 4
Two non-adjacent angles whose sum is 180° are supplementary.
60°
120°

7. PRACTICE: Angles 3 and 4 are supplementary
PRACTICE: Angles 3 and 4 are supplementary. The measure of angle 3 is 117°. Find angle 4. 3 4
117°
𝟔𝟑°
Definition of Supplementary Angles 𝑚∠3+𝑚∠4=180°
Substitute known values 117°+𝑚∠4=180°
Subtract − 117° − 117°
𝒎∠𝟒=𝟔𝟑°

8. LINEAR PAIR: Two adjacent angles whose sum is 180°.2
∠1 and ∠2 are a linear pair.

9. PRACTICE: Two angles form a linear pair
PRACTICE: Two angles form a linear pair. The measure of one angle is 5 times the measure of the other angle. Find the measure of each angle. 5𝑥
=5 30
=𝟏𝟓𝟎°
𝑥=𝟑𝟎° 5𝑥 𝑥
Definition of a linear pair 5𝑥+𝑥=180°
Combine like terms 𝑥=180°
Divide
𝒙=𝟑𝟎°

10. ∠1≅∠3 ∠2≅∠4 Vertical Angles:
VERTICAL ANGLES: The opposite angles formed by two intersecting lines or segments. 1 2 3 4 m g
∠1≅∠3
∠2≅∠4
Vertical Angles:

11. Linear Pairs: Vertical Angles:
PRACTICE: Identify all linear pairs and vertical angles in the figure below. 3 4 5 6 7
Linear Pairs:
Vertical Angles:
∠3 𝑎𝑛𝑑 ∠7
∠7 𝑎𝑛𝑑 ∠6
∠3 𝑎𝑛𝑑 ∠6

12. HOMEWORK #6:
Pg. 38: 4-43 odd, 46-52
REMINDER: turn in your Student Acknowledgment and Agreement Form!
If finished, work on other assignments:
HW #1: Pg. 5: 1, 5, 8-11, 13, 15, 17-21, 27-30, 46
HW #2: Pg. 12: 6-16, 21-28, 33, 35
HW #3: Pg. 19: 5-19, 25-27
HW #4: Pg. 20: 31-34, 43-45, 50-52
HW #5: Pg. 29: 7-27, 33-38, 45, 47, 50, 52, 62