Question

6. In triangle QRT, angle Q measures 80° and angle T measures 35°. Which list shows the side lengths of the triangle in order from greatest to least?
*
1 point
QT RT QR
RT QT QR
QT QR RT
RT QR QT

Answer 1

To determine the order of the side lengths in triangle QRT, we can use the relationship between angles and their opposite sides.

In triangle QRT:
- Angle Q = 80°
- Angle T = 35°

First, we can find angle R using the triangle sum theorem, which states that the sum of angles in a triangle is 180°:

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

Now we know the angles of the triangle:
- Angle Q = 80° (opposite side RT)
- Angle R = 65° (opposite side QT)
- Angle T = 35° (opposite side QR)

The side lengths opposite to these angles will follow the rule that the larger the angle, the longer the opposite side. Thus, we can list the sides in relation to the angles:

- Side opposite angle Q (RT) is the longest: RT
- Side opposite angle R (QT) is the second longest: QT
- Side opposite angle T (QR) is the shortest: QR

Therefore, the order of the side lengths from greatest to least is:
**RT, QT, QR**

So the correct choice is:
**RT, QT, QR**.