Question

1. question: an angle measures x + 50. its supplement measures 2x - 20. what is x?

• a. x = 50
• b. x = 45
• c. x = 60
• d. x = 70

1. question: angle theta and angle beta are supplementary. if angle theta = 15x - 30 and angle beta = 5x + 10, solve for x.

• a. x = 8
• b. x = 10
• c. x = 12

Explanation:

Step1: Use the property of supplementary angles

Supplementary angles sum to \(180^{\circ}\). So, \((x + 50)+(2x - 20)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(x+2x+50 - 20=180\), which gives \(3x+30 = 180\).

Step3: Solve for \(x\)

Subtract 30 from both sides: \(3x=180 - 30\), so \(3x=150\). Then divide both sides by 3: \(x=\frac{150}{3}=50\).

Step1: Use the property of supplementary angles

Since \(\theta\) and \(\beta\) are supplementary, \((15x - 30)+(5x + 10)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(15x+5x-30 + 10=180\), which gives \(20x-20 = 180\).

Step3: Solve for \(x\)

Add 20 to both sides: \(20x=180 + 20\), so \(20x=200\). Then divide both sides by 20: \(x=\frac{200}{20}=10\).

Answer:

A. \(x = 50\)