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 vertical angles? Wait, no, looking at the lines, actually, the angle \( (6x + 1)^\circ \), \( 79^\circ \), and \( (2x + 10)^\circ \) – wait, maybe the two horizontal lines are parallel? Wait, no, the vertical angles or supplementary? Wait, actually, let's see: the angle \( (2x + 10)^\circ \) and the angle adjacent to \( 79^\circ \) – wait, maybe the sum of \( (6x + 1)^\circ \), \( 79^\circ \), and \( (2x + 10)^\circ \) is 180? No, wait, maybe the angle \( (2x + 10)^\circ \) is equal to \( 79^\circ + (6x + 1)^\circ \)? No, that doesn't make sense. Wait, actually, looking at the diagram, the two horizontal lines are parallel, and the transversal creates alternate interior angles? Wait, no, maybe the angle \( (2x + 10)^\circ \) and the angle formed by \( (6x + 1)^\circ \) and \( 79^\circ \) are supplementary? Wait, let's re-examine.

Wait, the correct approach: the angle \( (2x + 10)^\circ \) is equal to \( (6x + 1)^\circ + 79^\circ \)? No, that would be if it's an exterior angle. Wait, no, actually, the two angles \( (6x + 1)^\circ \) and \( 79^\circ \) are adjacent to \( (2x + 10)^\circ \) such that \( (6x + 1) + 79 + (2x + 10) = 180 \)? Wait, no, maybe the angle \( (2x + 10)^\circ \) is a vertical angle to the sum of \( (6x + 1)^\circ \) and \( 79^\circ \). Wait, let's check the answer options. Let's try each option.

Wait, let's set up the equation. If we assume that \( (2x + 10) = (6x + 1) + 79 \)? No, that would be \( 2x + 10 = 6x + 80 \), \( -4x = 70 \), \( x = -17.5 \), which is not an option. So maybe the other way: \( (6x + 1) + (2x + 10) + 79 = 180 \)? Let's try that. \( 6x + 1 + 2x + 10 + 79 = 180 \), \( 8x + 90 = 180 \), \( 8x = 90 \), \( x = 11.25 \). Wait, that's one of the options. Let's check:

Step2: Set up the equation

Assuming the three angles \( (6x + 1)^\circ \), \( 79^\circ \), and \( (2x + 10)^\circ \) are supplementary (sum to \( 180^\circ \)):

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

Simplify the left side:

\( 6x + 1 + 79 + 2x + 10 = 8x + 90 \)

So:

\( 8x + 90 = 180 \)

Subtract 90 from both sides:

\( 8x = 180 - 90 \)

\( 8x = 90 \)

Divide both sides by 8:

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

Answer:

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