If BC = x − 2, CD = 19, and BD = 3x − 11, what is BD? Simplify your answer and write it as a proper fraction, mixed number, or integer. Could you please type the answer in a step by step.

UV = 15

BD= 31

Step-by-step explanation:

Since, U is the midpoint of TV.

Therefore,

TU = UV

x + 10 = 3x

x - 3x = - 10

-2x = - 10

x = - 10/-2

x = 5

UV = 3x = 3*5

UV = 15

BD = BC + CD

3x - 11 = x - 2 + 19

3x - 11 = x + 17

3x - x = 11 + 17

2x = 28

x = 28/2

x = 14

BD = 3x - 11 = 3*14-11 = 42 - 11

BD= 31

we know that

applying the law of sines

°

so

∠j=18°

∠k=29°

∠l=180-(18+29)=133°

the answer part a) is

the measure of angle k is  ≈29°

part b)  the measure of angle k could also be

(180-29)=151°

so

∠j=18°

∠k=151°

∠l=180-(18+151)=11°

the answer part b) is

the measure of angle k could also be 151°

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