What is the largest angle of a triangle if the angles form an arithmetic sequence and the smallest angle is 36 degrees?

Answer 1

If you had given the proper context of the question you would have got an answer much quicker.

You can't just copy the question bit without giving the background information - that contains vital information regarding the question. In this case it was the fact that the angles form an arithmetic sequence. I cannot see the paper/screen in front of you, nor can anyone else; we can only see what you type in as your question.

As there is a limited number of characters that can be used to ask a question you can't just copy the whole of the background information before the question as the question itself will get truncated off the end. You need to engage your brain and THINK about what the question is asking and what background information is needed and summarise it - as an example, look at how this question has been rewritten having found where you got your original question online - then it will be much easier for others to answer what you want, or you may actually realise what is needed anyway (can answer it yourself) and so improve your own cognitive reasoning and be better equipped to face the world.

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An arithmetic sequence is one where there is a set amount added between each term - a common difference.

Let the first angle be a

Let the common difference be d.

The the three angles are a, a+d, (a+d)+d = a + 2d

The sum of the three angles is: a + a + d + a + 2d = 3a + 3d = 3(a + d)

The sum of the angles of a triangle is 180°.

Thus:

3(a + d) = 180°

→ a + d = 60°

Now, we know the first angle a, which is the smallest angle at 36°

→ a + d = 60°

→ d = 60° - a

= 60° - 36°

= 24°

Now we can work out the largest angle, the last in the sequence, which is:

largest = a + 2d = 36° + 2 × 24° = 84°

Answer 2

Not enough information. It isn't clear how many angles there are in your problem, or how they are related. The only thing that can be stated is that the largest angle has a measure that is at least 36.

Answer 3

The answer depends on the shape to which the angles belong. However, in most cases, the answer is indeterminate due to insufficient information.

However, one of my colleagues worked hard to find what he thinks was the original question which you should have posted rather than lazily cut and paste some incomplete and incoherent phrases.

If the smallest angle in a triangle forms an arithmetic sequence and measures 36 deg then the other two angles are 36 + x and 36 + 2x deg. Together, these add to 3*(36 + x) deg which equals 180 deg.

=> 36 + x = 60 => x = 24 and so the largest angle is 36+2*24 = 84 deg.