To find the value of x in this scenario, let's break down the problem step by step.
First, we have an angle formed by two lines that create an "X" shape. We are told that the angle on one side of the X is (2x+24) degrees, and on the other side, it is 142 degrees.
Now, we know that the sum of the interior angles of any polygon is equal to (n-2) times 180 degrees, where n is the number of sides of the polygon. In this case, since we have an X shape, n = 4.
Since we have an X shape, it means that the lines forming the X intersect each other. When two lines intersect, they form vertical angles that are congruent (equal). In our case, the angle adjacent to (2x+24) degrees is also (2x+24) degrees.
Therefore, we can write the equation:
(2x+24) + (2x+24) + 142 + 142 = (4-2) * 180
Simplifying the equation:
4x + 312 = 2 * 180
4x + 312 = 360
4x = 360 - 312
4x = 48
x = 48/4
x = 12
Hence, the value of x is 12.