1. Naming Angles
Side/ray
Vertex
Side/ray

2. Naming Angles Ð 𝑀
32° 𝐴 𝐴 𝐷 ÐA
ÐDAM
ÐMAD
ÐDAM
ÐMAD

3. ≅ Angle Relationships Adjacent Angles Vertical Angles Congruent 30°
40°
“Angles on a line”
60°
15°
75°
50°
120°
60°
Complementary Angles
Supplementary Angles
90°
180°

4. ? ÐAEC & ÐCEF Four others ÐGED & ÐBED ÐAEC & ÐBED ÐCEB & ÐAED
Adjacent Angles
ÐAEC & ÐCEF
Four others
ÐGED & ÐBED
Vertical Angles
ÐAEC & ÐBED
ÐCEB & ÐAED
Complementary Angles
90°
ÐBED & ÐGED
Supplementary Angles
(angles on a line)
180° ?

5. Example A: 𝑥 +
132 =
180
−132
−132 𝑥 =
48° 48

6. Example B: 3 54 2 36 3𝑥 + 90 + 2𝑥 =
180 5𝑥 + 90 =
180
−90
−90 5𝑥 = 90 5 5 𝑥 = 18 18 18

7. Example C: 𝑥= 𝑦= 36
144
144
144 + 𝑥 =
180
−144
−144 𝑥 = 36 36

8. Example D: 69 3 3𝑥 + 16 = 85
−16
−16 3𝑥 = 69 3 3 𝑥 = 23 23

9. Example E: 90 + 𝑥 +
135 =
360
225 + 𝑥 =
360
−225
−225 𝑥 =
135
135

10. 103 + 59 + 𝑥+1 + 167 = 360 330 + 𝑥 = 360 −330 −330 𝑥 = 30 Example F:31
103 + 59 +
𝑥+1 +
167 =
360
330 + 𝑥 =
360
−330
−330 𝑥 = 30 30

11. Example G: The following two lines intersect
Example G: The following two lines intersect. The ratio of the measurements of the obtuse angle to the acute angle in any adjacent angle pair in this figure is 2∶1.
Determine the measure of each angle.
120°
2𝑥°
1𝑥° 2𝑥 + 1𝑥 =
180 3𝑥 =
180 3 3 𝑥 = 60
60°

12. Example H: The ratio of 𝑚∠𝐺𝐹𝐻 to 𝑚∠𝐸𝐹𝐻 is 2∶3.
Find the measures of ∠𝐺𝐹𝐻 and ∠𝐸𝐹𝐻. 𝐸 𝐻 3
54°
3𝑥° 2𝑥 + 3𝑥 = 90 2
2𝑥°
36° 𝐺 5𝑥 = 90 5 5 𝑥 = 18 18 18