Question

In the accompanying diagram, parallel lines AB and CD are intersected by transversal GH at points E and F, respectively. If angle AEG is (3x+7) and angle CFE is (4x - 2), find x.

Answer 1

By using the corresponding angles postulate, we found that angle AEG and angle CFE are congruent. Solving the equation 3x + 7 = 4x - 2 yields x = 9.

When parallel lines AB and CD are intersected by the transversal GH, we can use the corresponding angles postulate to link the angles formed.

Since AB is parallel to CD, angle AEG is congruent to angle CFE because they are corresponding angles.

Now, we know that angle AEG is (3x+7) degrees and angle CFE is (4x-2) degrees, and since these angles are congruent, we can set them equal to each other:

3x + 7 = 4x - 2

To solve for 'x', we'll first subtract 3x from both sides of the equation:

x - 2 = 7

Then, add 2 to both sides to isolate x:

x = 9

Once we found that x equals 9, we can plug it back into the expressions for either angle AEG or angle CFE to find the measure of those angles if needed.