Question

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.

Answer 1

Explanation:

2,3,5

Answer 2

2, 3, 5 are true statements

Explanation:

A diagram of the geometry is helpful. Our understanding of your description is shown in the first attachment. The second attachment shows how the various angles relate to each other. An exterior angle and its adjacent interior angle are a linear pair, so are supplementary.

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1. BEC is an exterior angle -- False, it is an interior angle

2. DEC is an exterior angle -- True

3. ABE and EBC are supplementary -- True, they are a linear pair

4. BCF and DEC are supplementary -- False, they are unrelated exterior angles

5. BEC is a remote interior angle to BCF -- True