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

In the diagram below, if < A = 100°, < B = 58°, < D = 100° and < F = 27°, we-example-1
User Moustapha
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1 Answer

25 votes
25 votes

ANSWER:

b. the two triangles are not similar

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

User DROP TABLE Users
by
2.9k points
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