Question

If m rst= 12x-1, m rsu = 9x-15 and m ust = 53 find each measure

Answer 1

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°