Answer: [tex]AC=41\°[/tex]
Step-by-step explanation:
The complete exercise is attached.
For this exercise it is important to remember that, by definition, if an angle formed by two intersecting chords has its vertex on a circle, this is called an "Inscribed angle".
The following formula is used to calculate the measure of an Inscribed angle:
[tex]Inscribed\ angle = \frac{1}{2}\ Intercepted\ Arc[/tex]
You can identify in the figure that:
[tex]Inscribed\ angle=ABC=(4x -3.5)\\\\Intercepted\ Arc=AC=(4x + 17)[/tex]
Then you can substitute values into the formula and solve for "x":
[tex](4x -3.5)= \frac{1}{2}(4x + 17)\\\\8x-7=4x+17\\\\4x=24\\\\x=6[/tex]
Then, AC is:
[tex]AC=(4(6)+ 17)\\\\AC=24+17\\\\AC=41\°[/tex]
