Answer:
x=17
Step-by-step explanation:
Hello! There are a few important pieces of information you need to keep in mind before trying to solve this problem:
- The angles in a triangle ALWAYS add up to 180 degrees.
- All vertical angles are congruent (I have attached a photo incase you aren't away of what vertical angles are)
Now that we know these two pieces of information, we can begin to set up our problem. Because the angles in a triangle always add up to 180, we can set up the problem as follows:
x + 100° + ∠DCE = 4x + 49° + ∠ACB
Now this is where the vertical angles come in. Angles ∠DCE and ∠ACB are vertical, which makes them congruent. Since they are the same value, we can subtract them from either side of the equation. (NOTE: We can only do this because they are the same value. Subtracting angles of different values will mess up your answer!!!)
Now, we have the same problem in much simpler terms. We can now simplify it in order to get x.
4x + 49 = x + 100 (subtract 49 from both sides)
4x = x + 51 (subtract x from both sides)
3x = 51 (divide both sides by 3)
x = 17 (FINAL ANSWER)
I really hope this helped! Take care! :)
