Question

1. question: angles a, b, and c form a straight line (they are supplementary). if angle a = 2x, angle b = 3x, and angle c = 4x, what is x?

• a. x = 20
• b. x = 15
• c. x = 25
• d. x = 30

1. question: angle 1 and angle 2 are adjacent and complementary. angle 1 measures x + 20. angle 2 measures 2x + 10. what is x?

• a. x = 20
• b. x = 30
• c. x = 25
• d. x = 40

1. question: angles 3 and 4 are vertical. if angle 3 = 8x - 1 and angle 4 = 5x + 38, what is x?

• a. x = 11
• b. x = 13
• c. x = 15
• d. x = 18

Explanation:

13.

Step1: Set up the equation

Since angles \(A\), \(B\), and \(C\) are supplementary (sum to \(180^{\circ}\)), we have \(2x + 3x+4x=180\).

Step2: Combine like - terms

\(9x = 180\).

Step3: Solve for \(x\)

Divide both sides by \(9\): \(x=\frac{180}{9}=20\).

Step1: Set up the equation

Since angle \(1\) and angle \(2\) are complementary (sum to \(90^{\circ}\)), we have \((x + 20)+(2x + 10)=90\).

Step2: Simplify the left - hand side

\(x+20 + 2x+10=3x + 30\). So, \(3x+30 = 90\).

Step3: Solve for \(x\)

Subtract \(30\) from both sides: \(3x=90 - 30=60\). Then divide by \(3\): \(x = 20\).

Step1: Set up the equation

Since angles \(3\) and \(4\) are vertical (equal in measure), we have \(8x-1=5x + 38\).

Step2: Move the \(x\) terms to one side

Subtract \(5x\) from both sides: \(8x-5x-1=38\), which simplifies to \(3x-1 = 38\).

Step3: Solve for \(x\)

Add \(1\) to both sides: \(3x=38 + 1=39\). Then divide by \(3\): \(x = 13\).

Answer:

A. \(x = 20\)

14.