Question

In the diagram below, if < A = 100°, < B = 58°, < D = 100° and < F = 27°, we can say that ___.

Answer 1

ANSWER:

b. the two triangles are not similar

STEP-BY-STEP EXPLANATION:

We know that the sum of all the internal angles of a triangle is equal to 180°, therefore, we calculate the third angle for each triangle as follows:

$\begin{gathered} \angle A+\angle B+\angle C=180 \\ \\ \angle C=180\degree-\angle A-\angle B \\ \\ \angle C=180\degree-100\degree-58\degree=22\degree \\ \\ \\ \operatorname{\angle}D+\operatorname{\angle}E+\operatorname{\angle}F=180\degree \\ \\ \operatorname{\angle}E=180\degree-\operatorname{\angle}D-\operatorname{\angle}F \\ \\ \operatorname{\angle}E=180\degree-100\degree-27\degree=53\degree \end{gathered}$

We can see that only the 100° angle in both triangles is the same and the others are different, therefore they are not similar.

So the correct answer is b. the two triangles are not similar