Question

Find the value of x. The diagram is not to scale. Lines f and g are parallel.

Answer 1

Lines f and g are parallel and the two angles are same-side angles, so they add up to 180 degrees. An equation for this would add up to 180, then solve for x to find the answer to the problem.

5x + (9x + 26) = 180, combine the like terms.

14x + 26 = 180, subtract 26 from both sides.

14x = 154, divide both sides by 14.

x = 11; so your answer is B. 11.

Answer 2

Using the knowledge of same-side interior angles, given that lines f and g are parallel, the value of x is: B. 11

Given that line f and line g are parallel to each other, the angles 5x and 9x + 26 are same-side interior angles.

Therefore:

$5x + (9x + 26) = 180^{\circ}$ (same-side interior angles are supplementary)

• Solve for x

$5x + 9x + 26 = 180$

• Add like terms

$14x + 26 = 180$

• Subtract 26 from both sides

$14x + 26 - 26 = 180 - 26 \\\\14x = 154$

• Divide both sides by 14

x = 11

Therefore, using the knowledge of same-side interior angles, given that lines f and g are parallel, the value of x is: B. 11

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