Question

circle all the problems that show two labeled angles that are supplementary. then find the value of x for only the circled problems.

1. (4x + 6)° 130°
2. (9x + 36)° 45°
3. (7x - 23)° 140°
4. (15x - 30)° 150°
5. (5x + 25)° 95°
6. 7x° (x + 4)°

Answer:

1. For problem 1:

• Explanation:
• Step1: Set up the equation
• Since the two - labeled angles \((4x + 6)^{\circ}\) and \(130^{\circ}\) are supplementary, their sum is \(180^{\circ}\). So the equation is \((4x + 6)+130 = 180\).
• Step2: Simplify the left - hand side of the equation
• Combine like terms: \(4x+(6 + 130)=4x + 136\). So the equation becomes \(4x+136 = 180\).
• Step3: Isolate the variable term
• Subtract 136 from both sides: \(4x=180 - 136\), so \(4x = 44\).
• Step4: Solve for \(x\)
• Divide both sides by 4: \(x=\frac{44}{4}=11\).

1. For problem 2:

• Explanation:
• Step1: Set up the equation
• Since the two - labeled angles \((9x + 36)^{\circ}\) and \(45^{\circ}\) are supplementary, we have \((9x + 36)+45 = 180\).
• Step2: Simplify the left - hand side of the equation
• Combine like terms: \(9x+(36 + 45)=9x + 81\). So the equation is \(9x+81 = 180\).
• Step3: Isolate the variable term
• Subtract 81 from both sides: \(9x=180 - 81\), so \(9x = 99\).
• Step4: Solve for \(x\)
• Divide both sides by 9: \(x=\frac{99}{9}=11\).

1. For problem 3:

• Explanation:
• Step1: Set up the equation
• Since the two - labeled angles \((7x - 23)^{\circ}\) and \(140^{\circ}\) are supplementary, we get \((7x - 23)+140 = 180\).
• Step2: Simplify the left - hand side of the equation
• Combine like terms: \(7x+( - 23+140)=7x + 117\). So the equation is \(7x+117 = 180\).
• Step3: Isolate the variable term
• Subtract 117 from both sides: \(7x=180 - 117\), so \(7x = 63\).
• Step4: Solve for \(x\)
• Divide both sides by 7: \(x=\frac{63}{7}=9\).

1. For problem 4:

• Explanation:
• Step1: Set up the equation
• Since the two - labeled angles \((15x - 30)^{\circ}\) and \(150^{\circ}\) are supplementary, we have \((15x - 30)+150 = 180\).
• Step2: Simplify the left - hand side of the equation
• Combine like terms: \(15x+( - 30+150)=15x + 120\). So the equation is \(15x+120 = 180\).
• Step3: Isolate the variable term
• Subtract 120 from both sides: \(15x=180 - 120\), so \(15x = 60\).
• Step4: Solve for \(x\)
• Divide both sides by 15: \(x=\frac{60}{15}=4\).

1. For problem 5:

• Explanation:
• Step1: Set up the equation
• Since the two - labeled angles \((5x + 25)^{\circ}\) and \(95^{\circ}\) are supplementary, we get \((5x + 25)+95 = 180\).
• Step2: Simplify the left - hand side of the equation
• Combine like terms: \(5x+(25 + 95)=5x + 120\). So the equation is \(5x+120 = 180\).
• Step3: Isolate the variable term
• Subtract 120 from both sides: \(5x=180 - 120\), so \(5x = 60\).
• Step4: Solve for \(x\)
• Divide both sides by 5: \(x=\frac{60}{5}=12\).

1. For problem 6:

• Explanation:
• Step1: Set up the equation
• Since the two - labeled angles \(7x^{\circ}\) and \((x + 4)^{\circ}\) are supplementary, we have \(7x+(x + 4)=180\).
• Step2: Simplify the left - hand side of the equation
• Combine like terms: \((7x+x)+4 = 8x+4\). So the equation is \(8x+4 = 180\).
• Step3: Isolate the variable term
• Subtract 4 from both sides: \(8x=180 - 4\), so \(8x = 176\).
• Step4: Solve for \(x\)
• Divide both sides by 8: \(x=\frac{176}{8}=22\).

The values of \(x\) for each problem are:

• Problem 1: \(x = 11\)
• Problem 2: \(x = 11\)
• Problem 3: \(x = 9\)
• Problem 4: \(x = 4\)
• Problem 5: \(x = 12\)
• Problem 6: \(x = 22\)