After setting the expressions for angles A and B equal and solving for x, we found the value of x to be 19. Substituting this value into the expressions for each angle, we determined m angle A and m angle B each to be 75 degrees, and m angle C to be 30 degrees.
We are given a triangle ABC where AC = CB, and we are asked to find the value of x and the measures of its angles given m angle A = (3x + 18), m angle B = (7x - 58), and m angle C = (2x - 8).
Since triangle ABC is isosceles with AC = CB, angles A and B are also equal. Therefore, we can set the expressions for m angle A and m angle B equal to each other to find x:
(3x + 18) = (7x - 58)
Now, we solve for x:
3x + 18 = 7x - 58
4x = 76
x = 19
With x found, we can substitute it back into the expressions for each angle:
m angle A = 3(19) + 18 = 57 + 18 = 75 degrees
m angle B = 7(19) - 58 = 133 - 58 = 75 degrees
m angle C = 2(19) - 8 = 38 - 8 = 30 degrees
Finally, we check that the sum of the angles in triangle ABC adds up to 180 degrees:
75 degrees + 75 degrees + 30 degrees = 180 degrees