In a right triangle, which pair of angles are $\mathrm{linear}\mathrm{pairs}$?

• A. The two $\mathrm{acute}$ angles
• B. The $\mathrm{right}$ angle and one of the $\mathrm{acute}$ angles
• C. All three angles together form a $\mathrm{linear}\mathrm{pair}$
• D. No pair of angles in a right triangle are $\mathrm{linear}\mathrm{pairs}$

Answer: (D)

Verified step by step guidance

1. Recall that a linear pair of angles are two adjacent angles whose non-common sides form a straight line, meaning they add up to 180 degrees and share a common vertex and side.
2. In a right triangle, the three angles are inside the triangle and sum up to 180 degrees, but none of the angles are adjacent in a way that their non-common sides form a straight line outside the triangle.
3. The two acute angles in a right triangle are not adjacent to each other; they are separated by the right angle, so they cannot form a linear pair.
4. The right angle and any one of the acute angles are also not adjacent in a way that their sides form a straight line; they meet inside the triangle and sum to 90 degrees, not 180 degrees.
5. Therefore, no two angles in a right triangle form a linear pair because linear pairs require the angles to be adjacent and supplementary (sum to 180 degrees), which does not happen inside the triangle.