Question

MATH HELP LEASE! WILL GIVE BRAINLIEST!

Answer 1

In a circle, the measure of an inscribed angle is half the measure of the intercepted arc.

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

AC = 4x+17
      = 4*6 + 17
      = 24 +17
      = 41°

Answer 2

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

$\angle{ABC}=\frac{1}{2} \text{arc(AC)}$

$(4x-3.5)^{\circ}=\frac{1}{2} (4x+17)^{\circ}$

$2*(4x-3.5)^{\circ}= (4x+17)^{\circ}$

$8x-7= 4x+17$

$4x=24$

$x=\frac{24}{4}$

$x=6$

So, Arc AC = (4x+17)° = (4*6+17)° = (24+17)° = 41°

Hence the measure of AC is 41°