Answer: (12) ∠1 = 20° (13) ∠2 = 50° (14) ∠3 = 15° (15) UV = 80° (16) AB = 40° (17) ABC or 180° - CD (18) BC - 140° (19) ABC = 150°
Step-by-step explanation:
12) [tex]\frac{1}{2}[/tex](UV - ST) = ∠1
[tex]\frac{1}{2}[/tex](80 - 40) = ∠1
[tex]\frac{1}{2}[/tex](40) = ∠1
20 = ∠1
13) [tex]\frac{1}{2}[/tex](UV + ST) = ∠2
[tex]\frac{1}{2}[/tex](70 + 30) = ∠2
[tex]\frac{1}{2}[/tex](100) = ∠2
50 = ∠2
14) [tex]\frac{1}{2}[/tex](VB - BS) = ∠3
[tex]\frac{1}{2}[/tex](60 - 30) = ∠3
[tex]\frac{1}{2}[/tex](30) = ∠3
15 = ∠3
15) [tex]\frac{1}{2}[/tex](UV - ST) = ∠1
[tex]\frac{1}{2}[/tex](UV - 20) = 30
UV - 20 = 60
UV = 80
16) ∠1 = arc AB
∠1 = 40
arc AB = 40
17) arc AB + arc BC = arc AC
= 180 = arc CD
18) ∠1 + ∠2 + ∠3 = 180
20 + ∠2 + 20 = 180
∠2 + 40 = 180
∠2 = 140
19) ∠1 + ∠ 2 = arc ABC
∠1 + ∠2 + ∠3 = 180
arc ABC + 30 = 180
arc ABC = 150
