Question

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

Explanation:

Step1: Use the property of parallel lines and transversal

When two parallel lines are cut by a transversal, the sum of an exterior angle and its adjacent interior angle is \(180^{\circ}\). So, \((6x + 1)+79 = 180\).

Step2: Simplify the equation

First, simplify the left - hand side of the equation: \(6x+1 + 79=6x + 80\). Then the equation becomes \(6x+80 = 180\).
Subtract 80 from both sides: \(6x=180 - 80\), so \(6x = 100\).

Step3: Solve for \(x\)

Divide both sides of the equation \(6x = 100\) by 6: \(x=\frac{100}{6}\approx16.67\) (This approach is wrong. Let's use the correct property of vertical angles and parallel lines).

Since the two lines are parallel, the sum of \((6x + 1)\) and \((2x+10)\) is equal to \(79\) (using the property of alternate - interior angles and angle addition).
So, \((6x + 1)+(2x+10)=79\).

Step4: Combine like terms

Combine the \(x\) terms and the constant terms: \(6x+2x+1 + 10=79\), which simplifies to \(8x+11 = 79\).

Step5: Isolate the variable \(x\)

Subtract 11 from both sides: \(8x=79 - 11\), so \(8x = 68\).
Divide both sides by 8: \(x=\frac{68}{8}=8.5\) (This is also wrong. Let's use the correct property: the sum of \((6x + 1)\) and \((2x + 10)\) is equal to \(180-79=101\) (linear - pair and alternate - interior angles).

The correct equation is \((6x + 1)+(2x+10)=180 - 79\).
Simplify the left - hand side: \(6x+2x+1 + 10=8x + 11\).
The right - hand side is \(101\). So, \(8x+11 = 101\).
Subtract 11 from both sides: \(8x=101 - 11\), \(8x = 90\), \(x = 11.25\).

Answer:

\(x = 11.25\)