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Step2247 [10]
3 years ago
6

Triangle ABC is shown below.

Mathematics
1 answer:
Andrew [12]3 years ago
8 0

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:

AB=AC\\\\2x=3x-7

Simplify the equation, solving for x. Add 7 to both sides:

2x+7=3x-7+7\\\\2x+7=3x

Subtract 2x from both sides:

2x-2x+7=3x-2x\\\\7=x

The value of x is 7. Insert the value of x into the given length of AC:

AC=3(7)-7

Simplify multiplication:

AC=21-7

Subtract:

AC=14

Therefore, the length of the line segment AC is 14.

:Done

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