Laura thinks that a triangle cannot have two obtuse angles.Do you agree? Explain your answer?
An obtuse angle is an angle larger than 90, the sum of the angles of a triangle is 180, then if one of the angles of a triangle is larger than 90 then the sum of the other angles is absolutely less than 90, therefore a triangle can have only one obtuse angle.
An obtuse angle is defined as greater than 90° and a triangle must have angles that add up to exactly 180°, nothing more or less. So if you have two angles that are obtuse, they will always add up to more than 180 making the third angle impossible. Therefore Laura is correct
To answer a bit more clearly & algebraically: if the 3 angles in a triangle are denoted: x, y & z and we assume the opposite of Lauras proposition, that 2 angles are obtuse (>90), can we solve for the 3rd angle? we know x + y + z = 180. .... (1) if assume x > 90 & y > 90 then it follows that x + y > 180 ..... (2) therefore by combining (1) & (2) we can imply that z < 0, and as all angles in a triangle must be greater than 0, the original proposition of being able to have 2 obtuse angles in a triangle must be impossible. Hence we must agree with Laura that a triangle cannot have two obtuse angles.
Obtuse angle -> larger than 90° Sum of all three angles -> 180° Can you get the answer from that?
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