What is the area of the shaded region in the figure above? Please help i don't understand triangles. Also can you explain how to solve this.

the area of the shaded region is 119.5

Step-by-step explanation:

area of a triangle formula 1/2bh (b= base) (h=height)

area of big triangle work

1/(20)(18)

20x18= 360

360 divided by 2 is 180 area of big triangle is 180

moving on to smaller triangle

1/2bh

1/2(11)(11)

121/2

60.5

THEN you subtract using bigger triangle by smaller

180-60.5=119.5

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

3 is greater then both of those numbers