Question

In the circle below, if AD is a diameter, and the arc BD = 6x - 9, and arc DC = 3x + 12, find x.

Answer 1

Answer:

The value of x = 7 (option D)

Step-by-step 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

`\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}`
`\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}`