Question

Given the line F is parallel to line g find the value of X. The diagram is not a scale

Answer 1

Check the picture below.

Answer 2

We can start by saying that since f and g are parallel, and that a line cuts through them, 3x+6x+45=180. This is due to the consecutive interior angles theorem, which states that if two parallel lines are cut by a transversal (another line), the interior angles the form from it (the angles between the parallel lines) are supplementary, or add up to 180 degrees. Therefore, we have 9x+45=180. Subtracting 45 from both sides using the subtraction property of equality, we get that 9x=135. Next, we can divide both sides by 9 to isolate x, resulting in x=15.

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