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1. a = 21°

2. b = 70°

3. c = 89°

Step-by-step explanation:

1. Determination of the value of a.

a = 21° (vertically opposite angles are equal)

2. Determination of the value of b.

From the question given above,

110 + b = 180 (sum of angles on a straight line)

Collect like terms

b = 180 – 110

b = 70°

3. Determination of the value of c.

a + b + c = 180 (sum of angles in a triangle)

a = 21°

b = 70°

c =?

21 + 70 + c = 180

91 + c = 180

Collect like terms

c = 180 – 91

c = 89°

step-by-step explanation:

try remembering the steps

∠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.