Answer:
The value of x = 7 (option D)
Explanation:
Given:
AD is a diameter
Arc BD= 6x - 9
arc DC = 3x + 12
To find:
the value of x
Arc BC = Arc BD + Arc DC
Arc BD and Arc DC are congruent
Arc BD = Arc DC
[tex]\begin{gathered} 6x\text{ - 9 = 3x + 12} \\ subtract\text{ 3x from both sides:} \\ 6x\text{ - }3x\text{ - 9 = 12} \\ 3x\text{ - 9 = 12} \end{gathered}[/tex][tex]\begin{gathered} add\text{ 9 to both sides:} \\ 3x\text{ - 9 + 9 = 12 + 9} \\ \\ 3x\text{ = 21} \\ divide\text{ both sides by 3:} \\ x\text{ = 21/3} \\ x\text{ = 7} \end{gathered}[/tex]
