Naming Angles Side/ray Vertex Side/ray

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

≅ 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°

? 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° ?  

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

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

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

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

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

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

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°

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