Question

In triangle QRT, angle Q measures 80 degrees and angle T measures 35 degrees. Which list shows the side lengths of the triangle in order from greatest to least.
A. QT RT QR
B. RT QT QR
C. QT QR RT
D. RT QR QT

Answer 1

To determine the order of the side lengths in triangle QRT based on the angles, we can use the property that the side opposite the largest angle is the longest side, and the side opposite the smallest angle is the shortest side.

Given:
- Angle Q = 80 degrees
- Angle T = 35 degrees

First, we need to find the measure of angle R:

- The sum of the angles in a triangle is 180 degrees.

\[
\text{Angle R} = 180 - \text{Angle Q} - \text{Angle T} = 180 - 80 - 35 = 65 \text{ degrees}
\]

Now we have the angles:
- Angle Q = 80 degrees (largest angle)
- Angle R = 65 degrees
- Angle T = 35 degrees (smallest angle)

Based on the angles, we can order the sides according to the angles they are opposite to:
- Side QR (opposite Angle T, 35 degrees) is the shortest.
- Side RT (opposite Angle R, 65 degrees) is medium length.
- Side QT (opposite Angle Q, 80 degrees) is the longest.

Thus, the order of the sides from greatest to least based on the angles is:
QT > RT > QR.

The correct answer is **A. QT RT QR**.