All the angles in a triangle add up to 180 degrees. With the isoceles triangle, two of the angles must be the same, so you could have these three angles: 50, 50, 80. (50+50+80=180)
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The 3rd angle is 80 degrees
The information was certainly known to Euclid.
The interior angles of any triangle (not traingle) always sum to 180 degrees. Whether or not it is equilateral (not eguilateral) is irrelevant.
The three angles inside every triangle, no matter what shape or size it is, always add up to 180 degrees.
In an isosceles triangle, two angles are equal. Since the angles provided are 54 degrees and 63 degrees, the equal angles must be 54 degrees. The sum of the angles in any triangle is 180 degrees. Thus, the measure of the third angle is calculated as follows: 180 - 54 - 54 = 72 degrees.