Answer:
x = 75
Step-by-step explanation:
Hi there!
Let's start by looking at the two parallel lines, l and m, and the diagonal line that crosses both of them. Line l and this diagonal line create the angle that measures (2x-30)°.
For a second, let's pretend that the 45°, x° and the straight line aren't there. The diagonal line and line m would create the alternate exterior angle of the angle that measures (2x-30)°. (Please see the attached image.)
Alternate exterior angles are equal in measure.
Now, with this knowledge, we now know that (2x-30)° is equal to 45+x:
2x-30 = 45+x
x-30 = 45
x = 75
Therefore, the value of x is 75.
To check your answer, you can substitute x into (2x-30)° and find the angle. It equals 120°. 45+75 is equal to 120°, so therefore, this answer is correct.
I hope this helps!
