Question
in triangle QRT, angle q measures 80 and angle t measures 35. which list shows the side lenghts 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
must show work
A. QT RT QR
B. RT QT QR
C. QT QR RT
D. RT QR QT
must show work
Answers
GPT-4o mini
In triangle QRT, we are given the measures of two angles: angle Q is 80 degrees and angle T is 35 degrees. To find the measure of angle R, we can use the fact that the sum of the angles in a triangle is always 180 degrees.
1. Calculate angle R:
\[
\text{Angle R} = 180^\circ - \text{Angle Q} - \text{Angle T} = 180^\circ - 80^\circ - 35^\circ = 65^\circ
\]
Now, we have the measures of all three angles:
- Angle Q = 80 degrees
- Angle R = 65 degrees
- Angle T = 35 degrees
2. To determine the order of the side lengths from greatest to least, we can recall the relationship between the angles and the sides of a triangle. The side opposite the largest angle is the longest, and the side opposite the smallest angle is the shortest.
- The largest angle is angle Q (80 degrees), so the side opposite it, side RT, will be the longest.
- The second largest angle is angle R (65 degrees), so the side opposite it, side QT, will be the second longest.
- The smallest angle is angle T (35 degrees), so the side opposite it, side QR, will be the shortest.
3. Based on this information, we can order the sides from greatest to least:
- Longest side: RT (opposite angle Q)
- Second longest: QT (opposite angle R)
- Shortest side: QR (opposite angle T)
Thus, the order of the side lengths from greatest to least is:
RT, QT, QR
Therefore, the answer is:
**D. RT, QT, QR.**
1. Calculate angle R:
\[
\text{Angle R} = 180^\circ - \text{Angle Q} - \text{Angle T} = 180^\circ - 80^\circ - 35^\circ = 65^\circ
\]
Now, we have the measures of all three angles:
- Angle Q = 80 degrees
- Angle R = 65 degrees
- Angle T = 35 degrees
2. To determine the order of the side lengths from greatest to least, we can recall the relationship between the angles and the sides of a triangle. The side opposite the largest angle is the longest, and the side opposite the smallest angle is the shortest.
- The largest angle is angle Q (80 degrees), so the side opposite it, side RT, will be the longest.
- The second largest angle is angle R (65 degrees), so the side opposite it, side QT, will be the second longest.
- The smallest angle is angle T (35 degrees), so the side opposite it, side QR, will be the shortest.
3. Based on this information, we can order the sides from greatest to least:
- Longest side: RT (opposite angle Q)
- Second longest: QT (opposite angle R)
- Shortest side: QR (opposite angle T)
Thus, the order of the side lengths from greatest to least is:
RT, QT, QR
Therefore, the answer is:
**D. RT, QT, QR.**