Question

Identifying Complementary Angles
Examine the intersection of these lines:

3 lines intersect to form 6 angles. Clockwise, from top left, the angles are A, B, C, D, E, F.

∠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: ∠B and ∠F, and ∠F and ∠E.

Reason: Opposite angles are equal, so A = D, B = E, C = F. The six angles sum to 360°, so 2(A + B + C) = 360° ⇒ A + B + C = 180°. Given B + C = 90°, therefore A = 180° − (B + C) = 90° (and D = 90°). Since F = C and E = B, B + F = B + C = 90° and F + E = C + B = 90°, so those pairs are complementary. The other listed pairs do not sum to 90°.