Asked by bob
Triangle E B C is shown with its exterior angles. Line E C extends through point F. Line C B extends through point A. Line B E extends through point D.
Which statements regarding the diagram of ΔEBC are true? Select three options.
∠BEC is an exterior angle.
∠DEC is an exterior angle.
∠ABE and ∠EBC are supplementary angles.
∠BCF and ∠DEC are supplementary angles.
∠BEC is a remote interior angle to exterior ∠BCF.
All Answers 1
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True statements (three):
- ∠DEC is an exterior angle.
Reason: D lies on the extension of BE past E, so ∠DEC is formed by the extension DE and EC and is an exterior angle at vertex E.
- ∠ABE and ∠EBC are supplementary angles.
Reason: A lies on the extension of BC past B, so AB and BC are a straight line; angles ABE and EBC form a linear pair and sum to 180°.
- ∠BEC is a remote interior angle to exterior ∠BCF.
Reason: ∠BCF is the exterior angle at C (CF is the extension of EC), and its remote interior angles are the interior angles at E and B; ∠BEC is one of those.
- ∠DEC is an exterior angle.
Reason: D lies on the extension of BE past E, so ∠DEC is formed by the extension DE and EC and is an exterior angle at vertex E.
- ∠ABE and ∠EBC are supplementary angles.
Reason: A lies on the extension of BC past B, so AB and BC are a straight line; angles ABE and EBC form a linear pair and sum to 180°.
- ∠BEC is a remote interior angle to exterior ∠BCF.
Reason: ∠BCF is the exterior angle at C (CF is the extension of EC), and its remote interior angles are the interior angles at E and B; ∠BEC is one of those.
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