Find the area of the shaded region.

1. If we join another radius to the shaded area, we will notice that the triangle has all sides 4 units, making it an equilateral triangle.

2. Equilateral triangle has all angles 60°

-

Area of 1 sector = 60/360 x π (4)² = 8.38 units²

-

-

Area of 1 shaded part = 8.38 - 6.93 = 1.45 units²

Area of all shaded part = 1.45 x 2 = 2.9 units²

-

2.9 units²

∠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.