what is the value of x if m arc ADC =5(x-3)and angle ABC=165

To find the value of x, we need to solve the equation involving the given information.

First, let's understand the information provided:

1. m arc ADC = 5(x-3): This equation tells us that the measure of arc ADC is equal to 5 times the quantity (x-3). So, we have an equation relating arc ADC to x.

2. angle ABC = 165: This is a separate piece of information given - the measure of angle ABC is 165 degrees.

Now, let's proceed with solving for x:

Since we do not have any direct relation between angle ABC and arc ADC, we cannot use the given angle to directly find the value of x.

However, we can try solving for x by setting up an equation using the properties of arcs and angles in a circle.

In any given circle, the measure of the central angle subtended by an arc is twice the measure of the intercepted arc. Therefore, we can write:

2 * m arc ADC = angle ABC

Substituting the given values into the above equation:

2 * (5(x-3)) = 165

Now we can solve this equation for x:

10(x-3) = 165
10x - 30 = 165
10x = 165 + 30
10x = 195
x = 195/10
x = 19.5

So, the value of x is 19.5.

To summarize the steps taken:
1. Set up the equation using the relationship between the measure of the central angle and the intercepted arc.
2. Plug in the given values to form an equation.
3. Simplify and solve for x.

Your School SUBJECT is probably math.