Question

(4x + 17)
What is the measure of AC ?
Enter your answer in the box.
(4x – 3.5)

Answer 1

Answer: 40 degrees

Step-by-step explanation: i took the test

Answer 2

Answer:
`AC=41\°`

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:

`Inscribed\ angle = (1)/(2)\ Intercepted\ Arc`

You can identify in the figure that:

`Inscribed\ angle=ABC=(4x -3.5)\\\\Intercepted\ Arc=AC=(4x + 17)`

Then you can substitute values into the formula and solve for "x":

`(4x -3.5)= (1)/(2)(4x + 17)\\\\8x-7=4x+17\\\\4x=24\\\\x=6`

Then, AC is:

`AC=(4(6)+ 17)\\\\AC=24+17\\\\AC=41\°`