Answer: angle x is 72 degrees.
Step-by-step explanation:
In the given diagram of triangles LMO and LNO, we need to find the value of angle x.
To find angle x, we can use the fact that the sum of angles in a triangle is 180 degrees. In triangle LMO, we have the angles L, M, and O. In triangle LNO, we have the angles L, N, and O.
Given information:
Angle M = 2x + 6
Angle L = 18 degrees
Angle N = 90 degrees
Angle O = 12 degrees
Now, we know that the sum of angles in a triangle is 180 degrees. We can set up an equation using this information for each triangle:
For triangle LMO:
L + M + O = 180
18 + (2x + 6) + 12 = 180
2x + 36 = 180
2x = 144
x = 72
Therefore, angle x is 72 degrees.
