Respuesta :

devishri1977

Answer:

x = 16

Step-by-step explanation:

 SR = ST ⇒ Two sides are equal. So, ΔSRT is an isosceles triangle.

The angles opposite to equal sides are equal.

  ⇒  ∠STR  = ∠R

       ∠STR = 4x - 28

Linear pair: If a ray stands on a line, then the adjacent angles are supplementary and they are called linear pair

∠STR + ∠STU = 180°    {linear pair}

4x - 28 + 9x = 180

4x + 9x - 28  = 180      {Combine like terms}

       13x- 28 = 180

Add 28 to both the sides

          13x    = 180 + 28

           13x  = 208

Divide both sides by 13

              x = 208/13

  [tex]\sf \boxed{x = 16}[/tex]

Answer:

x = 16

Step-by-step explanation:

since SR = ST , then Δ RST is isosceles with the 2 base angles congruent.

∠ STR = ∠ SRT = 4x - 28

∠ STR and ∠ STU are a linear pair and sum to 180° , that is

9x + 4x - 28 = 180

13x - 28 = 180 ( add 28 to both sides )

13x = 208 ( divide both sides by 13 )

x = 16

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