Find the area of the shaded region.

a. 36 square units
b. 32 square units
c. 17 square units
d. 16 square units

D. 16 square units

Step-by-step explanation:

Area of right angle triangle = (base*height)/2

Area of triangle with base = 5+4=9 and height = 8

square units

Area of triangle with base = 5 and height = 8

square units

Now subtracting the smaller area from larger area, we get the area of shaded portion.

Area = square units.

∠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.

1

x = 1

step-by-step explanation:

0 ÷ x = 0

0 ÷ 1 = 0