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Identify pairs of corresponding, alternate, and interior angles given that AB // CD.

Mathematics

ScanSolve AI Answer

Here are the solutions to the problems based on the figure where AB // CD:

a) 2 pairs of equal corresponding angles.
Corresponding angles are in the same relative position at each intersection.

i) ∠f=∠j\angle f = \angle j

ii) ∠e=∠i\angle e = \angle i
(Other valid pairs include: ∠g=∠k\angle g = \angle k, ∠h=∠l\angle h = \angle l, ∠b=∠n\angle b = \angle n, ∠a=∠m\angle a = \angle m, ∠c=∠o\angle c = \angle o, ∠d=∠p\angle d = \angle p)

b) 2 pairs of equal alternate angles.
Alternate angles are on opposite sides of the transversal.

i) ∠h=∠i\angle h = \angle i (Alternate interior angles)

ii) ∠c=∠n\angle c = \angle n (Alternate interior angles)
(Other valid pairs include: ∠g=∠j\angle g = \angle j, ∠b=∠o\angle b = \angle o for interior; ∠f=∠l\angle f = \angle l, ∠e=∠k\angle e = \angle k, ∠a=∠p\angle a = \angle p, ∠d=∠m\angle d = \angle m for exterior)

c) 2 pairs of interior angles which are supplementary.
Interior angles on the same side of the transversal are supplementary (add up to 180∘180^\circ).

i) ∠h+∠j=180∘\angle h + \angle j = 180^\circ

ii) ∠c+∠m=180∘\angle c + \angle m = 180^\circ
(Other valid pairs include: ∠g+∠i=180∘\angle g + \angle i = 180^\circ, ∠b+∠p=180∘\angle b + \angle p = 180^\circ)

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