Answer:
C.) 14
Step-by-step explanation:
Look at the triangle: angles b and c have the same arch, so they are congruent.
In a triangle, if two angles are congruent, then the triangle is isosceles, having two equal sides.
The sides opposite the congruent angles are congruent:
∠B → opposite side → AC
∠C → opposite side → AB
The sides AB and AC are equal. Make an equation:
[tex]AB=AC\\\\2x=3x-7[/tex]
Simplify the equation, solving for x. Add 7 to both sides:
[tex]2x+7=3x-7+7\\\\2x+7=3x[/tex]
Subtract 2x from both sides:
[tex]2x-2x+7=3x-2x\\\\7=x[/tex]
The value of x is 7. Insert the value of x into the given length of AC:
[tex]AC=3(7)-7[/tex]
Simplify multiplication:
[tex]AC=21-7[/tex]
Subtract:
[tex]AC=14[/tex]
Therefore, the length of the line segment AC is 14.
:Done
