Question

In the accompanying diagram, ĀB is parallel to CD, and AB and CD are cut by transversal EF at points G and H, respectively. If mZEGA = (2x + 30) and mZEHC = (x + 80), find x.

Answer 1

The value of x, which is the measure that satisfies the relation between the angled formed by parallel lines AB and CD cut by a transversal EF, is found to be 50.

Step-by-step explanation:

The given problem involves the concepts of parallel lines and transversals in geometry. When two parallel lines are cut by a transversal, the alternate interior angles are congruent. In this problem, AB is parallel to CD, and EF is the transversal. The angles m∆EGA and m∆EHC are alternate interior angles and therefore equal to each other when the lines ĀB and CD are parallel. Setting the expressions for the two angles equal to each other, we get:

(2x + 30) = (x + 80)

To find x, we solve the equation:

2x + 30 = x + 80

Subtract x from both sides:

x + 30 = 80

Then, subtract 30 from both sides:

x = 50