Answer:
x = 8
Step-by-step explanation:
1. First, we should realize that the angle with 16x + 7 and the angle with 5x + 5 are same-side interior angles, meaning they add up to 180 degrees. This means that 16x + 7 + 5x + 5 = 180.
2. (Solving)
Step 1: Simplify both sides of the equation.
- [tex](16x+5x)+(7+5)=180[/tex]
- [tex]21x + 12 = 180[/tex]
Step 2: Subtract 12 from both sides.
- [tex]21x + 12 - 12 = 180 - 12[/tex]
- [tex]21x = 168[/tex]
Step 3: Divide both sides by 21.
- [tex]\frac{21x}{21}=\frac{168}{21}[/tex]
- [tex]x = 8[/tex]
Step 4: Check if solution is correct.
- [tex]16(8)+7+5(8)+5=180[/tex]
- [tex]128 + 7 + 40 + 5 = 180[/tex]
- [tex]135 + 40 + 5 = 180[/tex]
- [tex]175 + 5 = 180[/tex]
- [tex]80= 80[/tex]
Therefore, x = 8.
