in triangle DEF, DE=EF and G is the midpoint of EF. if the measure of GDE=10 what is the measure of E?

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The measure of angle E is:

m∠E = 80°

Step-by-step explanation:

Given

The triangle ΔDEF

m∠GDE = 10°

DE = EF

G = midpoint of EF

To Determine

m∠E =?

Solving

As DE=EF and G is the midpoint of EF.

So, the right angle G is m∠DGE = 90°

as

We know that the sum of angles of a triangle is 180°.

m∠GDE + m∠DGE  + m∠E = 180°

10° + 90° + m∠E = 180°

m∠E = 180°  - 10 - 90

m∠E = 80°

Therefore, we conclude that the measure of angle E is:

1 is c

2 is a

3 is a

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.