Question

what is the value of x?
○ x = 2.25
○ x = 11.25
○ x = 13
○ x = 22
(2x + 10)°
(6x + 1)°
79°

Explanation:

Step1: Identify angle relationships

The angle \( (2x + 10)^\circ \) and \( 79^\circ \) are related, and also \( (6x + 1)^\circ \) and the angle equal to \( (2x + 10)^\circ \) (vertical angles or corresponding angles) along with \( 79^\circ \) form a linear relationship? Wait, actually, looking at the diagram, the two horizontal lines are parallel (since they are both horizontal), and the transversal creates angles. Wait, maybe the angle \( (2x + 10)^\circ \) and \( 79^\circ \) are such that \( (2x + 10) + 79 + (6x + 1) = 180 \)? Wait, no, maybe the angle \( (2x + 10)^\circ \) is equal to the angle adjacent to \( 79^\circ \) and \( (6x + 1)^\circ \). Wait, let's re-express:

Wait, the three angles: \( (6x + 1)^\circ \), \( 79^\circ \), and \( (2x + 10)^\circ \) should add up to \( 180^\circ \) because they are on a straight line (linear pair). So:

\( (6x + 1) + 79 + (2x + 10) = 180 \)

Combine like terms:

\( 6x + 2x + 1 + 79 + 10 = 180 \)

\( 8x + 90 = 180 \)

Subtract 90 from both sides:

\( 8x = 90 \)

Wait, that gives \( x = 11.25 \), which is one of the options. Let's check:

Wait, let's do the steps again:

Step1: Set up the equation

The sum of the three angles on a straight line is \( 180^\circ \). So:

\( (6x + 1) + 79 + (2x + 10) = 180 \)

Step2: Combine like terms

\( 6x + 2x + 1 + 79 + 10 = 180 \)

\( 8x + 90 = 180 \)

Step3: Solve for x

Subtract 90 from both sides:

\( 8x = 180 - 90 \)

\( 8x = 90 \)

Divide both sides by 8:

\( x = \frac{90}{8} = 11.25 \)

Yes, that matches the option \( x = 11.25 \).

Answer:

\( x = 11.25 \) (Option: \( x = 11.25 \))