Cumulative Standards Review
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Try to find the alternate interior angles. Use Theorem 3-1.
B
Looking through the given options, we can see that only B meets the requirements. Let's see why.
Second— a, b, and c each have the same measures as the triangle's angles. As we can see, ∠ b is one of the angles in the triangle. What about a and c? Let's recall Theorem 3-1. If a transversal intersects two parallel lines, the alternate interior angles are congruent. On the diagram, we are also given two parallel lines and two transversals, which makes angles ∠ a and ∠ e, and ∠ c and ∠ f, alternate interior angles.
Using the theorem written above, we can write the following conclusions. ∠ a ≅ ∠ e ∠ c ≅ ∠ f This means that angles ∠ a and ∠ e have the same measure, and ∠ c and ∠ f have the same measures too. Therefore, substituting ∠ e for a and ∠ f for c into the given expression, we get a sum which is equal to the given answer. a+b+c ⇔ ∠ e+b+∠ f This sum represents the sum of the angles in the triangle.
Therefore, the equivalent expression a+b+c can also be used to find the sum of the triangle's angles. The answer is B.