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In ΔSTU, \overline{SU} SU is extended through point U to point V, \text{m}\angle STU = (2x+8)^{\circ}m∠STU=(2x+8) ∘ , \text{m}\angle TUV = (7x-5)^{\circ}m∠TUV=(7x−5) ∘ , and \text{m}\angle UST = (x+19)^{\circ}m∠UST=(x+19) ∘ . What is the value of x?X?

Respuesta :

Answer:

The value of x is 8

Step-by-step explanation:

Refer the attached figure

[tex]\angle STU = (2x+8)^{\circ}\\\angle TUV = (7x-5)^{\circ}\\\angle UST = (x+19)^{\circ}[/tex]

[tex]\angle TUV[/tex] is an exterior angle

Exterior angle property : The sum of the two opposite interior angles is equal to the exterior angle

So,[tex]\angle TUV=\angle STU +\angle UST\\(7x-5)^{\circ}= (2x+8)^{\circ}+ (x+19)^{\circ}\\7x-5=3x+27\\7x-3x=27+5\\4x=32\\x=8[/tex]

Hence the value of x is 8

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