1. Find the value of x in the figure: The angles are supplementary angles. x + 20 + 120 = 180 x +140 = 180 x = 40° - 140 -140 120º (x + 20)°

2. ANGLE RELATIONSHIPS DAY 2

3. Vocabulary congruent vertical angles adjacent angles complementary angles supplementary angles

4. 1 2 To show that  1 is congruent to  2, we use arcs. Z X To show that there is a second set of congruent angles,  X and  Z, we use double arcs. X  ZX  Z This “arc” notation says that: When two angles are congruent they have the SAME measure. This “arc” notation says that: 1  21  2

5. When 2 lines intersect, they make vertical angles. 2 4 3 1

6. Vertical angles are opposite one another and are congruent. 2 4 3 1  1   3  2   4

7. Find the value of x in the figure: The angles are vertical angles. So, the value of x is 130°. 130° x°

8. Find the value of x in the figure: The angles are vertical angles. (x – 10) = 125 (x – 10)° 125° x – 10 = 125 x = 135° + 10 +10

9. Find the missing angle measures. 125° x° y° 15° B z D A C <ABD and <DBC are complementary angles, so m  ABD + m  DBC = 90° z + 15 = 90 -15 -15 z = 75° <PQR and <RQS are supplementary angles, so m  PQR + m  RQS = 180° 125 + y = 180 -125 y = 55° P Q R S T <PQR and <TQS are vertical angles. So, the value of x is 125°.

10. Adjacent angles are angles that: M J N R 1 2  1 and  2 are adjacent with the same vertex R and a common side A) share a common side, and B) have the same vertex Adjacent angles are “side-by-side”

11. Determine whether  1 and  2 are adjacent angles. No. They have no common side. 1 2 B 1 2 G Yes. They are “side-by-side”. N 1 2 J L No. They do not have a common vertex or a common side. The side of  1 is The side of  2 is

14. Practice: Angle Relationships worksheet