Respuesta :

chudung1976
You have known that: <RST=<RSQ+<QST
So we have 125°= (4x-7)+ (11x+12)
and 125°= 4x-7°+ 11x+12°
or 125°= 15x+5°
and 15x=125°-5°
and 15x=120°
By dividing by 15 we have x=120°:15= 8°
Have fun with x=8°

The value of x is 8.

Interior of Angle

The interior of an angle is the area between its two rays that define it.

Given to us,

∠RST = 125°,

∠RSQ = (4x-7)°,

∠QST = (11x+12)°,

Sum of ∠RSQ and ∠QST

As it is given to us that the point Q lies in the interior of ∠RST. therefore,

the sum of ∠RSQ and ∠QST is equal to ∠RST.

[tex]\angle RSQ + \angle QST = \angle RST\\(4x-7) + (11x+12) = 125\\4x - 7 + 11x +12 = 125\\15x +5 =125\\15x = 125-5\\15x = 120\\\\x=\dfrac{120}{15}\\\\x=8[/tex]

Hence, the value of x is 8.

Learn more about Interior of Angle:

https://brainly.com/question/25882965

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