Answer:
56
Step-by-step explanation:
1. We can use the exterior angle theorem to find the value of y. The exterior angle theorem states that the exterior angle of a triangle is equal to the sum of the two remote sides. This means that (y - 25) + (y + 12) = y + 43
2. (Solving)
Step 1: Simplify both sides of the equation.
- [tex]y + 43 = y - 25 + y + 12[/tex]
- [tex]y + 43 = (y+y)+(-25+12)[/tex]
- [tex]y + 43 = 2y -13[/tex]
Step 2: Subtract 2y from both sides.
- [tex]y + 43 - 2y = 2y - 13 - 2y[/tex]
- [tex]-y + 43 = 13[/tex]
Step 3: Subtract 43 from both sides.
- [tex]-y + 43 - 43 = 13 - 43[/tex]
- [tex]-y = -56[/tex]
Step 4: Divide both sides by -1.
- [tex]\frac{-y}{-1} = \frac{-56}{-1}[/tex]
- [tex]y = 56[/tex]
Step 5: Check if solution is correct.
- [tex](56) + 43 = (56) - 25 + (56) + 12[/tex]
- [tex]109 = 31 + 56 + 12[/tex]
- [tex]99 = 87 +12[/tex]
- [tex]99 = 99[/tex]
Therefore, y = 56.
