In triangle abc, angle a is congruent to angle c, ab= 10x-7, bc= 2x+33 and ac= 4x-6. find x

Since <A is congruent to <C , so triangle ABC is an isoceles triangle and side AB is congruent to BC.

AB = BC

Therefore, we can set up an equation as following:

10x - 7 = 2x + 33

10x - 7 - 2x = 2x + 33 -2x Subtracting 2x from each sides.

8x -7 = 33

8x - 7 + 7 = 33 + 7 Add 7 to each sides.

8x = 40

Divide each sides by 40.

So, x = 5