Respuesta :
Answer:
Option E - [tex](60^\circ, 45^\circ, 75^\circ)[/tex]
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) [tex](30^\circ, 40^\circ, 30^\circ)[/tex]
Sum of angles,
[tex]30^\circ+40^\circ+30^\circ=100^\circ[/tex]
No, this set is not a triangle.
B) [tex](42^\circ, 18^\circ, 130^\circ)[/tex]
Sum of angles,
[tex]42^\circ+18^\circ+130^\circ=190^\circ[/tex]
No, this set is not a triangle.
C) [tex](10^\circ, 15^\circ, 100^\circ)[/tex]
Sum of angles,
[tex]10^\circ+15^\circ+100^\circ=125^\circ[/tex]
No, this set is not a triangle.
D) [tex](40^\circ, 5^\circ, 40^\circ)[/tex]
Sum of angles,
[tex]40^\circ+5^\circ+40^\circ=85^\circ[/tex]
No, this set is not a triangle.
E) [tex](60^\circ, 45^\circ, 75^\circ)[/tex]
Sum of angles,
[tex]60^\circ+45^\circ+75^\circ=180^\circ[/tex]
Yes, this set is a triangle.
F) [tex](20^\circ, 40^\circ, 50^\circ)[/tex]
Sum of angles,
[tex]20^\circ+40^\circ+50^\circ=110^\circ[/tex]
No, this set is not a triangle.
Therefore, option E - [tex](60^\circ, 45^\circ, 75^\circ)[/tex] set represent angle measures that could be found in a triangle.
