Answer :
The sets of angle measures that can form a triangle are:
- [tex]\(50^\circ, 50^\circ, 50^\circ\)[/tex]
- [tex]\(25^\circ, 25^\circ, 40^\circ\)[/tex]
- [tex]\(35^\circ, 45^\circ, 95^\circ\)[/tex]
- [tex]\(40^\circ, 55^\circ, 85^\circ\)[/tex]
To form a triangle, the sum of the measures of any two angles must be greater than the measure of the third angle. Let's check each set of angles:
1. [tex]\(50^\circ, 50^\circ, 50^\circ\):[/tex]
- Yes, because [tex]\(50 + 50 > 50\)[/tex], all sides are equal.
2. [tex]\(25^\circ, 25^\circ, 40^\circ\):[/tex]
- Yes, because [tex]\(25 + 25 > 40\),[/tex] and [tex]\(25 + 40 > 25\).[/tex]
3. [tex]\(55^\circ, 25^\circ, 100^\circ\):[/tex]
- No, because [tex]\(55 + 25 < 100\),[/tex] the sum of the two smaller angles is not greater than the largest angle.
4. [tex]\(35^\circ, 45^\circ, 95^\circ\):[/tex]
- Yes, because [tex]\(35 + 45 > 95\)[/tex], and [tex]\(35 + 95 > 45\).[/tex]
5. [tex]\(40^\circ, 55^\circ, 85^\circ\):[/tex]
- Yes, because [tex]\(40 + 55 > 85\)[/tex], and [tex]\(40 + 85 > 55\).[/tex]
