Question

Please help it's very urgent thank you

Answer 1

Answer:  1) b. 20°    2) a. 4     3) a. 4    4) c. 34°

Step-by-step explanation:

1) Since TV bisects ∠STU, then ∠UTV = ∠STV and 2(∠UTV) = ∠STV

∠UTV = ∠STV

 x + 2 = $\dfrac{1}{4}x$+8

4x + 8 = x + 32                 multiplied by 4 to clear the denominator

3x + 8 =       32                  subtracted x from both sides

3x       =       24                  subtracted 8 from both sides

 x       =         8                  divided both sides by 3

2(∠UTV) = ∠STV

2(x + 2) = ∠STV

2(8 + 2) = ∠STV

  2(10)   = ∠STV

    20    = ∠STV

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2) Since SR bisects ST, then 2(SR) = ST

2(SR) = ST

2(3x + 3) = 30

  3x + 3  = 15            divided both sides by 2

  3x        = 12            subtracted 3 from both sides

    x         = 4             divided both sides by 3

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3) Since K is the midpoint of JL, then 2(JK) = JL

2(JK) = JL

 2(7) = 4x - 2

   14 = 4x - 2       multiplied 2 and 7

   16 = 4x            added 2 to both sides

    4 =  x              divided 4 from both sides

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4) Since QS is the midpoint, then 2(∠PQS) = ∠PQR

2(∠PQS) = ∠PQR

2(5y - 1)  = 8y + 12

10y - 2   = 8y + 12

 2y - 2   =        12           subtracted 8y from both sides

 2y        =        14            added 2 to both sides

   y        =         7             divided 2 from both sides

∠PQS = 5y - 1

          = 5(7) - 1

          =  35 - 1

          =    34