Answer:
Angle ABC should equal 68.8 degrees.
Step-by-step explanation:
You begin by finding the angle ACB. Which is 34. This is because we are given angle ACD = 146. ACD and ACB are supplementary angles so together they would equal 180. 180-146 = 34 hence why ACB is equal to 34. Next, we need to find the values for y in order to solve for angle ABC, we can do this by using this simple equation.
(5y+3) + (4y+8) = 146.
The reason we use 146 is that the measure of all interior angles in a triangle is 180 and since we already know one of those angles is 34 then the remaining 2 angles would add up to equal 146. Continuing on, using algebra we are able to understand that solution to this equation is y = 15.2 (repeating).
Finally, to solve for angle ABC we just need to replace y with the new value we found. The equation for this is, 4(15.2) + 8 = angle ABC. Through simple algebra, we are then able to find that angle ABC must equal 68.8
