Answer:
Option E - ![(60^\circ, 45^\circ, 75^\circ)](https://tex.z-dn.net/?f=%2860%5E%5Ccirc%2C%2045%5E%5Ccirc%2C%2075%5E%5Ccirc%29)
Step-by-step explanation:
Given : Each set of numbers below represents the measures of three angles.
To find : Which set represent angle measures that could be found in a triangle?
Solution :
We know that,
Sum of all three angles of triangle is 180°.
So whose sum is 180° that pair form a triangle.
A) ![(30^\circ, 40^\circ, 30^\circ)](https://tex.z-dn.net/?f=%2830%5E%5Ccirc%2C%2040%5E%5Ccirc%2C%2030%5E%5Ccirc%29)
Sum of angles,
![30^\circ+40^\circ+30^\circ=100^\circ](https://tex.z-dn.net/?f=30%5E%5Ccirc%2B40%5E%5Ccirc%2B30%5E%5Ccirc%3D100%5E%5Ccirc)
No, this set is not a triangle.
B) ![(42^\circ, 18^\circ, 130^\circ)](https://tex.z-dn.net/?f=%2842%5E%5Ccirc%2C%2018%5E%5Ccirc%2C%20130%5E%5Ccirc%29)
Sum of angles,
![42^\circ+18^\circ+130^\circ=190^\circ](https://tex.z-dn.net/?f=42%5E%5Ccirc%2B18%5E%5Ccirc%2B130%5E%5Ccirc%3D190%5E%5Ccirc)
No, this set is not a triangle.
C) ![(10^\circ, 15^\circ, 100^\circ)](https://tex.z-dn.net/?f=%2810%5E%5Ccirc%2C%2015%5E%5Ccirc%2C%20100%5E%5Ccirc%29)
Sum of angles,
![10^\circ+15^\circ+100^\circ=125^\circ](https://tex.z-dn.net/?f=10%5E%5Ccirc%2B15%5E%5Ccirc%2B100%5E%5Ccirc%3D125%5E%5Ccirc)
No, this set is not a triangle.
D) ![(40^\circ, 5^\circ, 40^\circ)](https://tex.z-dn.net/?f=%2840%5E%5Ccirc%2C%205%5E%5Ccirc%2C%2040%5E%5Ccirc%29)
Sum of angles,
![40^\circ+5^\circ+40^\circ=85^\circ](https://tex.z-dn.net/?f=40%5E%5Ccirc%2B5%5E%5Ccirc%2B40%5E%5Ccirc%3D85%5E%5Ccirc)
No, this set is not a triangle.
E) ![(60^\circ, 45^\circ, 75^\circ)](https://tex.z-dn.net/?f=%2860%5E%5Ccirc%2C%2045%5E%5Ccirc%2C%2075%5E%5Ccirc%29)
Sum of angles,
![60^\circ+45^\circ+75^\circ=180^\circ](https://tex.z-dn.net/?f=60%5E%5Ccirc%2B45%5E%5Ccirc%2B75%5E%5Ccirc%3D180%5E%5Ccirc)
Yes, this set is a triangle.
F) ![(20^\circ, 40^\circ, 50^\circ)](https://tex.z-dn.net/?f=%2820%5E%5Ccirc%2C%2040%5E%5Ccirc%2C%2050%5E%5Ccirc%29)
Sum of angles,
![20^\circ+40^\circ+50^\circ=110^\circ](https://tex.z-dn.net/?f=20%5E%5Ccirc%2B40%5E%5Ccirc%2B50%5E%5Ccirc%3D110%5E%5Ccirc)
No, this set is not a triangle.
Therefore, option E -
set represent angle measures that could be found in a triangle.