Question

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Answer 1

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°

Explanation:

12)
`(1)/(2)`(UV - ST) = ∠1

`(1)/(2)`(80 - 40) = ∠1

`(1)/(2)`(40) = ∠1

20 = ∠1

13)
`(1)/(2)`(UV + ST) = ∠2

`(1)/(2)`(70 + 30) = ∠2

`(1)/(2)`(100) = ∠2

50 = ∠2

14)
`(1)/(2)`(VB - BS) = ∠3

`(1)/(2)`(60 - 30) = ∠3

`(1)/(2)`(30) = ∠3

15 = ∠3

15)
`(1)/(2)`(UV - ST) = ∠1

`(1)/(2)`(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