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 \(112.5^\circ\).
Similar Questions
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Important Questions from Triangles
In a Δ ABC, if ∠A = 120° and AB = AC, then the values of ∠B and ∠C are respectively:
The product of the perimeter of a triangle, the radius of its in‐circle, and a number gives the area of the triangle. The number is
In ∆ABC, 2∠A = 3∠B = 6∠C. What is the value of the largest angle among these three angles?
The longest side in a right-angled triangle is called :
The sum of two sides of a triangle with the third side is
