Question

Examine the intersection of these lines:


∠B and ∠C are complementary angles.
∠E and ∠F are complementary angles.

Which of the following other pairs of angles are complementary? Select all that apply.

∠A and ∠C

∠B and ∠F

∠C and ∠D

∠F and ∠E

∠D and ∠F​

Answer 1

Answer:2 and 4

Explanation:

^B and ^F

^F and ^E

Answer 2

• ∠B and ∠F
• ∠F and ∠E . . . already listed in the problem statement, so may not be considered an "other pair"

Explanation:

∠C and ∠F are vertical angles, so are congruent. Then any angle complementary to one of those will also be complementary to the other.

Likewise, ∠B and ∠E are vertical angles and congruent. Any angle complementary to one of them will also be complementary to the other. Here, ∠E and ∠F are listed as complementary, so we know ∠B and ∠F will be also.