If the measure of arc AD = (6x -80)° and <G = (x + 2)°, what is the measure of <G?​

Answer: [tex]\angle G=23\°[/tex]Step-by-step explanation: Remember that an inscribed angle is defined as an angle formed by two chords and whose vertex lies on the circle. By definition, the measure of an inscribed angle is: [tex]Inscribed\ Angle=\frac{Intercepted\ Arc}{2}[/tex] You know that: [tex]Intercepted\ Arc=AD = (6x -80)\\\\Inscribed\ Angle=\angle G=(x + 2)[/tex] Then, you need to substitute values and solve for "x": [tex](x+2)=\frac{(6x -80)}{2}\\\\2(x+2)=6x-80\\\\2x+4=6x-80\\\\4+80=6x-2x\\\\84=4x\\\\x=\frac{84}{4}\\\\x=21[/tex] Substituting the value of "x" into [tex]\angle G=(x + 2)\°[/tex] you get:  [tex]\angle G=(21 + 2)\°=23\°[/tex]