Find area of the composite figure..

627square inches

Step-by-step explanation:

Area of the composite figure.. = area of triangle + area of parallelogram

Since the triangle is an equilateral triangle;

Area of the triangle = r²sintheta

Area of the triangle = 18²sin60

Area of the triangle = 324sin60

Area of the triangle  = 324(0.8860)

Area of the triangle = 280.584 square in

Area of the triangle = 281 square inches

Area of parallelogram = absintheta

Area of parallelogram = 20(20)sin60

Area of parallelogram = 400(0.8660)

Area of parallelogram = 346.4square inches

Area of parallelogram = 346 square inches

Area of the figure = 346  + 281

Area of the figure  = 627square inches

lo.lll

step-by-step explanation:

∠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.