Hello.
This is how I would work out this question, please let me know if there are any flaws.
Write an equation:
9x+24+30x=180
We know that a straight line is an 180 degree angle, so both angles should have a sum of 180.
Now, we solve algebraically.
9x+24+30x=180
39x+24=180
39x+24-24=180-24
39x=156
39x/39=156/39
x= 4
Substitute 4 for x in each expression.
9x+24
9(4)+24
36+24
60
So, the first angle is 60 degrees.
30x
30(4)
120
The second angle is 120 degrees.
Angle AEB is opposite angle DEC, so that means it has the same value of 60 degrees.
∴The answer is 60 degrees.
Please check it over and try other ways of solving to make sure I have the correct answer. I tried my best, hope this helps!
