In triangle ABC, the measure of angle A is 35° and the measure of angle B is 20°. In triangle DEF, the measure of angle D is 35° and the measure of angle F is 125°. Which of the following explains whether triangles ABC and DEF are similar.
A).By Triangle Angle Sum Theorem, angle C is 55°. So, the triangles are similar because two corresponding angles have the same measure, which satisfies the Angle-Angle Triangle Similarity Theorem.
B).By Triangle Angle Sum Theorem, angle C is 125°. So, the triangles are similar because two corresponding angles have the same measure, which satisfies the Angle-Angle Triangle Similarity Theorem.
C).By Triangle Angle Sum Theorem, angle C is 155°. So, the triangles are similar because two corresponding angles have the same measure, which satisfies the Angle-Angle Triangle Similarity Theorem.
D).By Triangle Angle Sum Theorem, angle C is 135°. However, the triangles are not similar because only two corresponding angles have the same measure, which is not enough to satisfy the Angle-Angle Triangle Similarity Theorem.