ACT Math · Angles and polygons

Two parallel lines are cut by a transversal. One angle formed measures 112°. What is the measure of the co-interior (same-side interior)…

ℓ₁ℓ₂112°
Two parallel lines are cut by a transversal. One angle formed measures 112°. What is the measure of the co-interior (same-side interior) angle to it?

Answer and explanation

Answer: J: 68°

Co-interior (same-side interior) angles formed by parallel lines and a transversal are supplementary, so they sum to 180∘180^\circ. The angle that is co-interior with the given 112∘112^\circ angle is 180∘−112∘=68∘180^\circ-112^\circ=68^\circ, choice J. Choice F (112∘112^\circ) is the measure of an angle that is congruent to the given one, such as a corresponding or alternate interior angle, rather than the co-interior one. Choice G (78∘78^\circ) and choice H (28∘28^\circ) do not relate to 112∘112^\circ by any parallel-line rule. The two angles must add to a straight angle, so the answer has to be acute here.

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