Question

Point C is the center of the circle. The measure of angle ACB is 12x – 7. Arc ADB measures 10x – 7. Find the value of x.

Answer 1

We are asked to solve for the value of x given that the center is the point C and the ∠ACB is 12x-7 while the given arc is equal to 10x-7. To solve this problem, we need to remember that the summation of angle ACB and angle ADB is equal to 360°. Hence, the solution is shown below:
∠ACB + ∠ADB = 360°
12X - 7 + 10X -7 = 360 , combine same term such as:
22x - 14 = 360 , transpose -14 to the right side such as:
22x = 360 + 14
22x = 374 , divide both sides bu 22
22x/ 22 = 374 / 22
x = 17

The answer to this problem is 17 and this is the value of x.