To solve the problem, we must first understand the angle relationships involved in the construction that Nathan performed.
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Nathan constructs ray \( BX \), which is the angle bisector of \( \angle ABC \). Since the measure of \( \angle ABC \) is given as \( 84^\circ \), this means that \( \angle ABX = \angle XBC = \frac{84^\circ}{2} = 42^\circ \).
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Next, Nathan constructs ray \( BY \) as the angle bisector of \( \angle XBC \). We already determined that \( \angle XBC = 42^\circ \). Therefore, when we bisect this angle, the angle measurements will be:
- \( \angle XBY = \angle YBC = \frac{42^\circ}{2} = 21^\circ \).
As a result, the measurement of \( \angle YBC \) is:
\[ \angle YBC = 21^\circ \]
Thus, the correct answer is:
d. 21 degrees.
1 answer