Question

Which statements regarding the diagram of ΔEBC are true? Check all that apply.

∠BEC is an exterior angle.
∠DEC is an exterior angle.
∠ABE and ∠EBC are supplementary angles.
∠BCF and ∠BEC are supplementary angles.
∠BEC is a remote interior angle to exterior ∠BCF.

Answer 1

(2),(3) and (5)

Explanation:

It is given that BEC is a triangle, then ∠BEC is an interior angle of the triangle BEC and not the exterior angle, thus option (1) is incorrect.

In the given triangle, ∠DEC is an exterior angle as it is outside the given triangle BEC, thus option (2) is correct.

In the given triangle, ∠ABE+∠EBC=180°,(Straight line property) thus ∠ABE and ∠EBC are supplementary angles. Hence, option (3) is correct.

In the given triangle,∠BCF and ∠BEC do not form supplementary angles. Hence, option (4) is incorrect.

In the given triangle, ∠BEC is an interior angle of the triangle BEC to exterior ∠BCF. Hence, option (5) is correct.

Answer 2

In the given diagram, BEC is the interior angle . And angles ABE and EBC are linear pair . And sum of measurement of angles of linear pair is 180 degree.

There is no relationship between angles BCF and BEC .

And for the exterior angle BCF, angle BEC is a remote interior angle . And DEC is a exterior angle .

So statements second, third and fifth are true statements .