To find the measure of \(\angle BIC\) in triangle \(ABC\) where \(BI\) and \(CI\) are angle bisectors of \(\angle ABC\) and \(\angle ACB\), we can use the following geometric property of angle bisectors:
The measure of the angle formed by two internal angle bisectors of a triangle, namely \(\angle BIC\), is given by:
\(\angle BIC = 90^\circ + \frac{1}{2} \angle BAC\).
Given that \(\angle BAC = 45^\circ\), we can substitute this value into the formula:
| \(\angle BIC\) = 90° + 0.5 × 45° |
| \(\angle BIC\) = 90° + 22.5° |
| \(\angle BIC\) = 112.5° |
Hence, the measure of \(\angle BIC\) is \(112.5^\circ\).
The correct answer is \(112.5^\circ\).
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