Question

What is the value of x? Enter your answer in the box. x = in. A bow tie shape polygon made of two bow ties that share a vertex. The shape is created by two segments intersecting forming two triangles with vertical angles. The smaller triangle is on the left side and the larger triangle is on the right side. On the smaller triangle, the left side is labeled 5 inches, the north side is labeled 8 inches. On the bigger triangle, the right side is labeled 15 inches. The south sides of the triangle is labeled x. An alternate interior angle of the triangles are marked congruent to each other.

Answer 1

thats awnser is right i have k12

Explanation:

Answer 2

x=24 inches

Explanation:

From the given information, consider ABCDE be the bow shaped polygon created by two segments intersecting forming two triangles with vertical angles that is ∠ACB=∠DCE.

AB=5 in, AC=8 in , CE=x inches and DE= 15 inches.

Now, From ΔABC and ΔDCE,

∠ACB=∠DCE(Vertically opposite angles)

∠BAC=∠DEC(Alternate angles)

Therefore, by AA similarity, ΔABC is similar to ΔDCE.

Thus, by using Proportionality theorem, we get

`(DE)/(AB)=(EC)/(CA)`

⇒
`(15)/(5)=(x)/(8)`

⇒
`3=(x)/(8)`

⇒
`x=24 inches`