Question

In Triangle ABC, with DE parallel to BC, if AD = 6x - 7, DB = 4x - 3, AE = 3x - 3, and EC = 2x - 1, find x.

(a) 4
(b) 5
(c) 6
(d) 7

Answer 1

To find x in Triangle ABC with DE parallel to BC, we can set up an equation based on the corresponding angles. Solving the equation, we find that x is equal to 4 / 3.

Step-by-step explanation:

To find x in Triangle ABC, we need to set up an equation based on the given information. Since DE is parallel to BC, we can use the concept of parallel lines and transversals to find corresponding angles. Since angles ADE and ABC are corresponding angles, they are congruent. Therefore, we can set up the following equation:

3x - 3 = 6x - 7

Simplifying this equation, we get:

3x - 6x = -7 + 3

-3x = -4

Dividing both sides of the equation by -3, we get:

x = -4 / -3

x = 4 / 3

Therefore, x is equal to 4 / 3, which is not one of the given answer choices.