If the measure of arc AC is 76^circ and the mangle ABC=2x-12 what is the value of x? x=25 x=13 x=44 x=38

# Explanation<br /><br />To solve for \( x \) in the given problem, we need to understand the relationship between the measure of the arc \( AC \) and the angle \( \angle ABC \).<br /><br />In a circle, the measure of an inscribed angle is half the measure of the intercepted arc. Therefore, if \( \angle ABC \) intercepts arc \( AC \), then:<br /><br />\[<br />m \angle ABC = \frac{1}{2} m \text{arc} AC<br />\]<br /><br />Given:<br />- The measure of arc \( AC \) is \( 76^\circ \).<br />- \( m \angle ABC = 2x - 12 \).<br /><br />Using the relationship between the inscribed angle and the intercepted arc, we have:<br /><br />\[<br />m \angle ABC = \frac{1}{2} \times 76^\circ = 38^\circ<br />\]<br /><br />Since \( m \angle ABC = 2x - 12 \), we can set up the equation:<br /><br />\[<br />2x - 12 = 38<br />\]<br /><br />To solve for \( x \), follow these steps:<br /><br />1. Add 12 to both sides of the equation:<br /><br />\[<br />2x - 12 + 12 = 38 + 12<br />\]<br /><br />\[<br />2x = 50<br />\]<br /><br />2. Divide both sides by 2:<br /><br />\[<br />x = \frac{50}{2}<br />\]<br /><br />\[<br />x = 25<br />\]<br /><br />Therefore, the value of \( x \) is 25.<br /><br /># Answer<br /><br />\( x = 25 \)