Question

describing supplementary angle relationships continued 7 (7x - 21)° (9x + 1)° 8 (5x + 5)° (6x + 10)° 9 (20x + 30)° (15x + 10)° 10

Explanation:

Step1: Recall supplementary - angle property

Supplementary angles add up to 180°.

Step2: Solve for x in problem 7

Set up the equation $(7x - 21)+(9x + 1)=180$.
Combine like - terms: $7x+9x-21 + 1=180$, which simplifies to $16x-20 = 180$.
Add 20 to both sides: $16x=180 + 20=200$.
Divide both sides by 16: $x=\frac{200}{16}=12.5$.

Step3: Solve for x in problem 8

Set up the equation $(5x + 5)+(6x + 10)=180$.
Combine like - terms: $5x+6x+5 + 10=180$, which simplifies to $11x+15 = 180$.
Subtract 15 from both sides: $11x=180 - 15 = 165$.
Divide both sides by 11: $x = 15$.

Step4: Solve for x in problem 9

Set up the equation $(15x + 10)+(20x+30)=180$.
Combine like - terms: $15x+20x+10 + 30=180$, which simplifies to $35x+40 = 180$.
Subtract 40 from both sides: $35x=180 - 40 = 140$.
Divide both sides by 35: $x = 4$.

Step5: Solve for x in problem 10

Set up the equation $(12x+16)+(18x + 14)=180$.
Combine like - terms: $12x+18x+16 + 14=180$, which simplifies to $30x+30 = 180$.
Subtract 30 from both sides: $30x=180 - 30 = 150$.
Divide both sides by 30: $x = 5$.

Answer:

Problem 7: $x = 12.5$
Problem 8: $x = 15$
Problem 9: $x = 4$
Problem 10: $x = 5$