Answer:
The measure of AC is 41°
Step-by-step explanation:
Given : ∠ABC = (4x-3.5)°
Arc AC = (4x+17)°
An inscribed angle: An angle with its vertex on the circle and whose sides are chords.
The intercepted arc : The arc that is inside the inscribed angle and whose endpoints are on the angle.
The Inscribed Angle Theorem : The measure of an inscribed angle is half the measure of its intercepted arc.
Uisng the theorem
[tex]\angle{ABC}=\frac{1}{2} \text{arc(AC)}[/tex]
[tex](4x-3.5)^{\circ}=\frac{1}{2} (4x+17)^{\circ}[/tex]
[tex]2*(4x-3.5)^{\circ}= (4x+17)^{\circ}[/tex]
[tex]8x-7= 4x+17[/tex]
[tex]4x=24[/tex]
[tex]x=\frac{24}{4}[/tex]
[tex]x=6[/tex]
So, Arc AC = (4x+17)° = (4*6+17)° = (24+17)° = 41°
Hence the measure of AC is 41°
