Respuesta :

akposevictor

Answer:

x = 13

m<RST = 155°

m<RSU = 102°

Step-by-step explanation:

m<RST = (12x - 1)°

m<RSU = (9x - 15)°

m<UST = 53°

m<UST + m<RSU = m<RST (angle addition postulate)

53 + (9x - 15) = (12x - 1) (substitution)

Solve for x

53 + 9x - 15 = 12x - 1

53 - 15 + 9x = 12x - 1

38 + 9x = 12x - 1

Subtract 12x from each side

38 + 9x - 12x = 12x - 1 - 12x

38 - 3x = - 1

Subtract 38 from each side

38 - 3x - 38 = -1 - 38

-3x = -39

Divide both sides by -3

x = 13

m<RST = (12x - 1)°

Plug in the value of x

m<RST = 12(13) - 1 = 156 - 1 = 155°

m<RSU = (9x - 15)°

m<RSU = 9(13)x - 15 = 117 - 15 = 102°

The measures of each angle are:

m<RSU = 102°

m<RST = 155°

m<UST = 53°

The given parameters are:

m<RST  =  (12x  -  1)°

m<RSU =  (9x - 15)°

m<UST =   53°

Note that:

m<RST  =  m<RSU  +  m<UST

Substitute m<RST  =  12x  -  1, m<RSU =  9x - 15, and m<UST =   53 into the equation above in order to solve for x

m<RST  =  m<RSU  +  m<UST

12x - 1  =  9x - 15   +  53

12x - 9x  =  -15 + 53 + 1

3x   =  39

x  =  39/3

x  =  13

To find the measure of <RST, substitute x = 3 into m<RST = 12x - 1

m<RST = 12(13) - 1

m<RST = 155°

To find the measure of <RSU, substitute x = 3 into m<RSU = 9x - 15

m<RSU = 9(13) - 15

m<RSU = 102°

Learn more on angles here: https://brainly.com/question/14362353

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