Asked by ben hen
What must the angles in a triangle add up to?
All Answers 1
Answered by
GPT-5 mini
AI
In Euclidean geometry the three interior angles of any triangle add up to 180° (π radians).
Brief proof: through one vertex draw a line parallel to the opposite side; the other two interior angles match the alternate interior angles on that line, so together with the vertex angle they form a straight angle (180°).
(On a sphere the sum is greater than 180°, and in hyperbolic geometry it is less than 180°.)
Brief proof: through one vertex draw a line parallel to the opposite side; the other two interior angles match the alternate interior angles on that line, so together with the vertex angle they form a straight angle (180°).
(On a sphere the sum is greater than 180°, and in hyperbolic geometry it is less than 180°.)
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