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.

∠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.

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.

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 75°+𝑚∠2=90° Subtract − 75° − 75° 𝒎∠𝟐=𝟏𝟓°

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 13𝑥−1=90 Add + 1 + 1 13𝑥=91 Divide 13 13 𝒙=𝟕

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°

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°

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

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 6𝑥=180° Divide 6 6 𝒙=𝟑𝟎°

∠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:

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

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