Angles in a Triangle
The triangle shown in the image has two angles equally marked: angle B and angle C are congruent.
When two angles (exactly two) are congruent in a given triangle, then it's an isosceles triangle, where the congruent sides are those who form the congruent angles.
In our problem, segment AB and AC are congruent because they are the equal sides of the isosceles triangle. Thus:
2x = 3x - 7
Subtracting 3x
-x = -7
Multiplying by -1
x = 7
Now we have the value of x, we'll find the side length AC:
AC = 3x - 7 = 3*7 - 7 = 21 - 7 = 14
Answer: 14
