Consider the measures of
∠3 and
∠4 in the figure below
The measure of ∠3 is equal to the measure of ∠1 because they are corresponding angles for the parallel lines
l and m intersected by the transversal line t. Similarly, the measure of
∠3 is equal to the measure of ∠4 because they are corresponding angles for the parallel lines s and t intersected by the transversal line m. Since the measure of
∠1 is
35°, the measures of
∠3 and
∠4 are also
35°. Since
∠4 and
∠2 are supplementary, the sum of the measures of these two angles is 180°. Therefore, the measure of ∠2 is
180°−35°=145°.
Choice A is incorrect because 35° is the measure of
∠1, and
∠1 is not congruent to
∠2. Choice B is incorrect because it is the measure of the complementary angle of
∠1, and
∠1 and
∠2 are not complementary angles. Choice C is incorrect because it is double the measure of
∠1.