Can an equilateral triangle have an obtuse angle? - MywallpapersMobi

Can an equilateral triangle have an obtuse angle?

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Science & Mathematics

Mathematics

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Is it possible to draw an obtuse equilateral triangle. explain.?


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Best Answer: 
Hey there!

No. An equilateral triangle is always acute. The reason is the equilateral triangle consists of congruent sides and congruent angles.

Let x= the measure of the first angle.

By the Triangle Sum Theorem:

x+x+x=180 –>
3x=180 –>
x=60°

That means every angle in the equilateral triangle measures 60°. This violates the obtuse triangle, as one of the angles measures more than 90°.

Therefore, there is no such thing as an obtuse equilateral triangle.

Hope it helps!

?

· 1 decade ago

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  • jest

    Obtuse Equilateral Triangle
    Source(s):
    https://shrink.im/a9OAY

    jest
    · 2 years ago

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  • Puzzling

    An obtuse triangle has one angle that is greater than 90°.

    An equilateral triangle has 3 equal angles all 60°. Therefore by definition you cannot draw an obtuse equilateral triangle. An equilateral triangle will always be acute.


    Puzzling
    · 1 decade ago

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  • dehl

    Equilateral Acute Triangle
    Source(s):
    https://shrinks.im/a8I5U

    dehl
    · 2 years ago

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  • Meags

    No it is not. There are 180 degrees total in a triangle. If it is an equilateral triangle, then each angle is 180/3=60 degrees. An obtuse angle must be greater than 90 degrees therefore it is not possible.

    Meags
    · 1 decade ago

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  • Pascal

    No, an equilateral triangle will be equiangular, and since the angles of a triangle will add up to 180°, each angle of an equilateral triangle will be 180°/3 = 60°, making it an acute triangle, not obtuse.

    Pascal
    · 1 decade ago

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  • James L

    No, I is not possible. An equilateral triangle will always have the same number of degrees which is 60. If you have even 1 obtuse angle then that means all the sides of the triangle wont be equal.
    Source(s):
    Took Math A

    James L
    · 1 decade ago

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  • Rec

    Impossible.

    to be an equilateral triangle, each of the 3 angles must be 60 degrees.

    and 60 degrees is not an obtuse angle

    Rec
    · 1 decade ago

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  • Hiroko

    This Site Might Help You.

    RE:
    is it possible to draw an obtuse equilateral triangle. explain.?

    Source(s):
    draw obtuse equilateral triangle explain: https://shortly.im/qwuwx

    Hiroko
    · 3 years ago

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  • PammingSodom

    No. An equilateral triangle will always have three 60 degree angles, so no angle can have a measure greater than 90 degrees.

    PammingSodom
    · 1 decade ago

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Can an equilateral triangle have an obtuse angle?

I’m thinking not, because all sides must be equal, but
does that also imply that all angles are equal?

Chris

 


Hi Chris. You are right – an equilateral triangle cannot have an obtuse angle. In fact, the angles are all "fixed" – they are each 60 degrees.

Try this: take three equal length pencils and form a triangle. Now take three more pencils and try to form a triangle that has angles different from the first. Don’t try too hard of course: it isn’t actually possible.

In fact, in any triangle when you have even two sides the same length, that means their opposite angles are also the same size. That’s an isosceles triangle. An equilateral triangle has all three sides the same, therefore all three angles are the same. When you add up the angles of any triangle, you get 180 degrees, so 180 divided by 3 is 60 – the size of every angle of any equilateral triangle.

Stephen La Rocque>