Question

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

Answer 1

Answer: $AC=41\°$

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:

$Inscribed\ angle = \frac{1}{2}\ Intercepted\ Arc$

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":

$(4x -3.5)= \frac{1}{2}(4x + 17)\\\\8x-7=4x+17\\\\4x=24\\\\x=6$

Then, AC is:

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