Here is a figure where ray [i]r[/i] meets line [i]l[/i]. The dashed rays are angle bisectors.[br][br][img]data:image/png;base64,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[/img][br][br][br]Diego made the conjecture: “The angle formed between the angle bisectors is always a right angle, no matter what the angle between [i]r[/i] and [i]l[/i] is.” [br][br]It is difficult to tell specifically which angles Diego is talking about in his conjecture. Here is a labeled diagram and a rephrasing of Diego's conjecture with more specific details:[br][br][list][*]We're given that ray [i]CE[/i] bisects angle [i]ACD[/i] into two congruent angles that each measure [i]a[/i] degrees.[/*][*]We're given that ray [i]CF[/i] bisects angle [i]DCB[/i] into two congruent angles that each measure [i]b[/i] degrees.[/*][*]Diego concludes that angle [i]ECF[/i] is a right angle, in other words [i]a[/i] + [i]b[/i] = 90 degrees.[/*][/list][br][br][br][img]data:image/png;base64,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[/img][br][br]Use the labeled diagram to explain why Diego's conjecture is true.
Yes, Diego’s conjecture is true. Angle ACB forms a line, and so measures 180 degrees.[br]That means 2a + 2b = 180.[br]Dividing each side by 2, we have a + b = 180.[br]The expression a+b can be interpreted to represent the measure of angle ECF, and so angle ECF is a right angle. This argument works no matter the particular values of a and b, so long as those values make sense with the constraints of the figure.