Question

1. question: two angles form a straight line. one angle measures 2x + 10 and the other measures 3x - 5. what is x?

• a. x = 35
• b. x = 42
• c. x = 50
• d. x = 65

1. question: a linear pair consists of angles measuring 12x and 6x. find the value of x.

• a. x = 15
• b. x = 10
• c. x = 8
• d. x = 20

Explanation:

Step1: Use the property of angles forming a straight line

Angles forming a straight line sum to \(180^{\circ}\). So, \((2x + 10)+(3x - 5)=180\).

Step2: Simplify the left - hand side

Combine like terms: \(2x+3x + 10 - 5=180\), which gives \(5x+5 = 180\).

Step3: Isolate the term with \(x\)

Subtract \(5\) from both sides: \(5x+5-5=180 - 5\), so \(5x=175\).

Step4: Solve for \(x\)

Divide both sides by \(5\): \(x=\frac{175}{5}=35\).

Step1: Use the property of a linear pair

A linear pair of angles sum to \(180^{\circ}\). So, \(12x+6x = 180\).

Step2: Simplify the left - hand side

Combine like terms: \(18x=180\).

Step3: Solve for \(x\)

Divide both sides by \(18\): \(x=\frac{180}{18}=10\).

Answer:

A. \(x = 35\)