Final answer:
To find the measure of angle A, we can use the fact that the sum of the angles in a triangle is 180 degrees. By setting up an equation and solving for x, we can find the value of angle A.
Step-by-step explanation:
To find the measure of angle A, we can use the fact that the sum of the angles in a triangle is 180 degrees. So, we have the equation (2x - 24) + (x - 8) + (4x + 49) = 180. We can solve for x by combining like terms and then solve for angle A by substituting the value of x back into the expression for angle A.
Simplifying the equation gives 7x + 17 = 180. Subtracting 17 from both sides gives 7x = 163. Dividing both sides by 7 gives x = 23. Substituting x = 23 into the expression for angle A gives angle A = (2*23 - 24) = 22 degrees.