Solve for x. Enter your answer in the box. x = A triangle with vertices labeled as A, C, D. Side C D is the base and the top vertex is A. Side C D is parallel to B E. Side A E is labeled as 7x minus 40, side E D is labeled as 18, side C B is labeled as 15, and side A B is labeled as 25.

x = 10

Step-by-step explanation:

In ΔADC

∵ EB / / DC

∴ m∠AEB = m∠ADC ⇒ corresponding angles

∴m∠ABE = m∠ACD ⇒ corresponding angles

In the two triangles ADC, AEB

∵ m∠AEB = m∠ADC

∵ m∠ABE = m∠ACD

∵ ∠A is a common angle

∴ ΔADC similar to ΔAEB

∴ AE/AC = AB/AC

∵ AE = 7x - 40, ED = 18

∴ AD = 7x - 40 + 18 = 7x - 22

∵ AB = 25, BC = 15

∴ AC = 25 + 15 = 40

∴ (7x - 40) / (7x - 22) = 25/40 ⇒ use cross multiplication

∴ 40 (7x - 40) = 25 (7x - 22)

∴ 280x - 1600 = 175x - 550

∴ 280x - 175x = 1600 - 550

∴ 105x = 1050

∴ x = 1050 : 105 = 10