Re: In th triangle ABC, the measure of angle A is 25° and the m
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13 Aug 2021, 15:35
In addition to the awesome answers provided, I might humbly add mine.
Process
1. B > 90, so as B gets greater, C gets smaller.
2. This means, when B is smallest, C is greatest. In this case, we'll cheat a little bit to ease calculations and treat B's "smallest" value as being 90 degrees.
3. So, for the sake of simplicity, let's assume that angle B is actually 90 degrees (it can't actually be 90 degrees by the parameters of the problem, but this will give us a figure to go forward from).
4. The internal angles of a triangle add up to 180 degrees. Therefore, 25 + 90 + C = 180.
5. That means that C = 65 in that example.
6. Since B will always be greater than 90, C will always be less than 65.
7. A, B, C, and D all fit the bill!
Cool tip:
The sum of the internal angles of any figure is equal to (n-2)*180 where n is the number of sides in the figure. This can be used when the problem involves figures other than a triangle.