A20° sector in a circle has an area of 21.5π yd². what is the area of the circle? use 3.14 for pi. enter your answer as a decimal in the box.

The area of circle is 1215.18 yd²

Step-by-step explanation:

A 20° sector in a circle has an area of 21.5π yd²

Formula:

Where,

Area of sector = 21.5π yd²

Angle of sector = 20°

Now we will find the area of circle.

Hence, The area of circle is 1215.18 yd²

∠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.