Question

In a triangle ABC, angle A is congruent to angle C, AB= 10x-7, BC=2x+33, and AC= 4x-6. Find x.

Answer 1

(10x - 7) + (2x + 33) + (4x - 6) = 180 -- the angles in an isolesces triangle = 180 degrees
combine like terms
16x + 20 = 180
16x = 180 - 20
16x = 160
x = 160/16
x = 10

I am not the best at geometry, so you might better get a second opinion

Answer 2

typo * isosceles

Answer 3

am I way off on this ?

Answer 4

AB = 10x - 7 : 10(10) - 7 : 100 - 7 = 93
BC = 2x + 33 : 2(10) + 33 : 20 + 33 = 53
AC = 4x - 6 : 4(10) - 6 : 40 - 6 = 34

93 + 53 + 34 = 180

Answer 5

but I am not getting two of the same angles...

Answer 6

$$
\cfrac{\sin C}{10x-7}=\cfrac{\sin A}{2x+33}\\
$$
But, \(\sin C=\sin A\), so by the Law of Sines:
$$
1=\cfrac{10x-7}{2x+33}\\
2x+33=10x-7\\
2x-10x=-7-33\\
-7x=-40\\
x=\cfrac{40}{7}
$$

Answer 7

I thought A and C were the base angles making it an isosceles triangle ? I am totally off track here.....

Answer 8

They are -- A and C are the base angles making an isosceles triangle. So the segments opposite them are equal: \(2x+33=4x-6\).

Answer 9

so if 40/7 was plugged in for x, all 3 angles would equal 180 ??

Answer 10

AB, AC and BC are all lengths from each of the vertices, not angles. If they had been angles, the problem would have stated angle A, angle B and angle C when referencing them.