Find the value of x if m arc adc=5(x-3) and angle abc=165 degrees.
To find the value of x in the given equation, we need to understand the relationship between the measurements of an angle and its corresponding arc in a circle.
In a circle, the measure of an inscribed angle (angle abc) is equal to half the measure of its intercepted arc (arc adc). Therefore, we can write the equation as follows:
m(arc adc) = 2 * m(angle abc)
Given that m(angle abc) = 165 degrees, we can substitute it into the equation:
5(x - 3) = 2 * 165
Now, we can solve for x:
5(x - 3) = 330
Distribute the 5:
5x - 15 = 330
Add 15 to both sides:
5x = 345
Divide both sides by 5:
x = 69
Therefore, the value of x is 69.