Question

in triangle QRT angle Q measure 80 and angle T measure 35 which list shows the side lengths of the triangle in order from greatest to least

Answer 1

To determine the side lengths of triangle QRT from greatest to least, we first need to find the measure of angle R. The sum of the angles in a triangle is always 180 degrees.

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

We can find angle R as follows:

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

Now, we have the measures of all angles in triangle QRT:
- Angle Q = 80 degrees
- Angle R = 65 degrees
- Angle T = 35 degrees

In a triangle, the longest side is opposite the largest angle, and the shortest side is opposite the smallest angle. Therefore, the ordering of the angles and their corresponding opposite sides is as follows:

- Angle Q (80 degrees) is the largest → side RT is the longest
- Angle R (65 degrees) is in the middle → side QT is the next longest
- Angle T (35 degrees) is the smallest → side QR is the shortest

So, the order of the sides from greatest to least is:
1. Side RT (opposite angle Q)
2. Side QT (opposite angle R)
3. Side QR (opposite angle T)

Thus, the side lengths of triangle QRT in order from greatest to least are: **RT, QT, QR**.