Question

Show interior angle theorem step by step

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Answer 1

Answer:

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Step-by-step explanation:

m∠8=180°−m∠1 =m∠2 . Therefore, ∠2≅∠8 . You can prove that ∠3≅∠5 using the same method. The converse of this theorem is also true; that is, if two lines k and l are cut by a transversal so that the alternate interior angles are congruent, then k∥l .

Answer 2

Since k || 1, by the Corresponding Angles Postulate,

angle 1 ≈ angle 5.

Therefore, by the definition of congruent angles,

m angle 1 = m angle 5

Since angle 1 and angle 2 form a linear pair, they are supplementary, so

m angle 1+ m angle 2 = 180°.

Also, 25 and 28 are supplementary, so

m/ angle 5+m angle 8 = 180°.

Substituting m angle 1 for m angle 5, we get

m angle 1+m/ angle 8 = 180°.

Subtracting m angle 1 from both sides, we have

m angle 8= 180° - m angle 1

= m angle 2

Therefore, angle 2 = 28.

You can prove that angle 3 = angle 5 using the same method.

hope it helps you