Explain why a triangle cannot have more than one obtuse angle.

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geometry2

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Jyotsana's profile pic

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Triangle cannot have more than one obtuse angle because there are 3 side and if you add three sides it equals to 180 degree and obtuse angle is greater than 90 degree and the other two has to be less than 90 degree.

giorgiana1976's profile pic

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We'll consider the three angles of triangle as: A,B,C.

By definition, the sum of angles of a triangle is 180 degrees.

A+B+C = 180 degrees

We'll consider A as being the obtuse angle of the triangle ABC.

Therefore A>90 degrees.

Since A>90 degrees, then B+C < 90.

This tells us that B and C are acute angles.

Therefore, a triangle cannot have more than one obtuse angle.

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