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Given The Diagram Below, What Must C Measure (in Degrees) In Order For ABC To Be Isosceles?

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Vin Ginge answered
No details have been provided in the question, but an isosceles triangle has two sides and two angles equal. The equal angles lie opposite to the equal sides.
If the remaining (unequal) angle is A then the two equal angles each measure (180 - A) ÷ 2.
If one of the equal angles (B) is known then the remaining (unequal) angle measures 180 - 2B.

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