Question

A conjecture and the flowchart proof used to prove the conjecture are shown.

Answer 1

Answer:

∠1 is supplementary to ∠3.

Step-by-step explanation:

Given information: ABCD is a parallelogram.

Prove: ∠1 is supplementary to ∠3.

Proof:

∠1 = ∠ADB

∠2 = ∠DBC

∠3 = exterior angle adjacent to angle D B C.

Statement                                         Reason

∠2 is supplementary to ∠3           Linear pairs

m∠2+m∠3=180°                             Definition of supplementary angles

$m\angle 1=m\angle 2$                            Alternative interior angles

m∠1+m∠3=180°                              Substitute property of equality

∠1 is supplementary to ∠3            Definition of supplementary angles

Hence proved.