Question

Which angles are supplementary to each other? Select all that apply.

Answer 1

Answer: Option B

Explanation:

Supplementary angle are the angles that when gets added up, it becomes 180°. Each of the angles are supplement to each other. Hence, to check the supplementary angles we have to first carefully observe the diagram given.

1. Option -1- In the option, it telling that ∠DEA and ∠DEB are supplementary angles. By carefully observing it you see ∠DEA and ∠DEB are the obtuse angles. You can say that it is not a supplementary angle. As generally two obtuse angle cannot make up to form a supplementary angle. Hence, Option-1 is incorrect.
2. Option-2-In the option, it telling that ∠BEC and ∠DEB are supplementary angles. By carefully observing it you see that ∠BEC is a acute angle and ∠DEB is a obtuse angle. If you remove EA ray, you see that this two angle form a supplementary angle i.e 180° angle. Hence, option-2 is correct.
3. Option-3-In the option, it telling that ∠BEC and ∠AEC are supplementary angles. By carefully observing it you see that ∠BEC and ∠AEC are acute angles. If you remove DE ray, you see that this two angles become only a acute angle i.e acute angle ≠ 180°. Hence, option-3 is incorrect.
4. Option-4-In the option, it telling that ∠DEA and ∠BEC are supplementary angles. By carefully observing it you see that these angles are not adjacent angles as a supplementary angle should be a adjacent angle. Hence, option-4 is incorrect.

Therefore, Option B is correct.