Question

If the triangle is equiangular then, it is an obtuse angle triangle. Which of the following statements doesn’t convey the same meaning as in this mentioned sentence?
(a) A triangular is equiangular only if it is an obtuse-angle triangle.
(b) If a triangle is not an obtuse-angled triangle, then it is not an equiangular triangle.
(c) Equi Angularity is a sufficient condition for a triangle to be obtuse-angled.
(d) A triangle is only an obtuse-angled triangle if it is equiangular.

Answer 1

Hint: We will use the link words to rewrite a sentence; they are If, And, Then, etc., like this, we have to use these link words to rewrite the given sentence in different ways and check whether the given options contain the re-written sentences. From that, we can find which sentence means less from the given options.

Complete step-by-step solution:
It is given that, If the triangle is equiangular then it is an obtuse-angled triangle. Now we will rewrite this sentence using the link-words.
Let us write some sentences using the link word if.
1) A triangular is equiangular only if it is an obtuse-angle triangle.
2) A triangle is only obtuse-angled if it is equiangular.
In the above two sentences, the first sentence gives the same meaning as in the given question. Thus, it is a correct sentence. The second sentence also gives the same meaning as it is in the given question. Thus, it is also a correct option.
Therefore, option (a) and option (d) have the right meaning.
Now let us rewrite the given sentence again.
The above sentence is also giving the same meaning as it is in the given question. Thus, this is also a correct sentence.
Therefore, option (c) has the right meaning.
The last option (b) If a triangle is not an obtuse-angled triangle, then it is not an equiangular triangle.
This sentence doesn’t give the correct meaning thus this is the incorrect sentence.
Hence, Option (b) is the correct answer, as it contains a sentence that has incorrect meaning.

Note: In this problem, we aim to find the sentence that doesn’t convey the same meaning as it is in the given sentence. We have to use the link word to get sentences of the same meaning. Many sentences can be found using ink words but we only found the sentences that were given in the option to make it simpler.