Question

Provide the missing statements and reasons for the following proof:

Answer 1

The missing statements and reasons to proof that ∠1 is supplementary to ∠3 are:

• R2: Definition of corresponding angles
• R3:  Corresponding angles postulate
• R5: Supplement Postulate
• S7:  m∠1 + m∠3 = m∠2 + m∠3
• S8:  m∠1 + m∠3 = 180° (∠1 is supplementary to ∠3)

What are Supplementary Angles?

• Supplementary angles, when added together will give us a sum of 180°.
• Linear pair angles and corresponding angles are supplementary.

Thus, to prove that ∠1 is supplementary to ∠3:

We are given that lines m and n are parallel.

∠1 and ∠3 are corresponding angles.

So therefore, ∠1 = ∠3 by the corresponding angles postulate.

∠2 and ∠3 are linear pair, their sum therefore equals 180° based on the definition of supplementary angles.

Based on the substitution property, we have the following:

m∠2 + m∠3 = m∠1 + m∠3

m∠1+m∠3=180°

Therefore, ∠1 is supplementary to ∠3 based on the definition of supplementary.

The missing statements and reasons to proof that ∠1 is supplementary to ∠3 are:

• R2: Definition of corresponding angles
• R3:  Corresponding angles postulate
• R5: Supplement Postulate
• S7:  m∠1 + m∠3 = m∠2 + m∠3
• S8:  m∠1 + m∠3 = 180° (∠1 is supplementary to ∠3)

Learn more about supplementary angles on:

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