Answer:
x = 55
Step-by-step explanation:
1. We can use exterior angle theorem to find the value of x. The exterior angle theorem states that the exterior angle of a triangle is equal to the sum of the two remote angles in that same triangle.
- Given the information above, x + 39 = x - 16 + x
2. (Solving)
Step 1: Simplify both sides of the equation.
- [tex]x+39=(x+x)+(-16)[/tex]
- [tex]x+39=2x-16[/tex]
Step 2: Subtract 2x from both sides.
- [tex]x+39-2x=2x-16-2x[/tex]
- [tex]-x + 39 = -16[/tex]
Step 3: Subtract 39 from both sides.
- [tex]-x + 39 - 39 = -16 - 39[/tex]
- [tex]-x = -55[/tex]
Step 4: Divide both sides by -1.
- [tex]\frac{-x}{-1} = \frac{-55}{-1}[/tex]
- [tex]x = 55[/tex]
Step 4: Check if solution is correct.
- [tex](55)+39=(55)-16+(55)[/tex]
- [tex]94 = 39 + 55[/tex]
- [tex]94 = 94[/tex]
Therefore, x = 55.
