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Which sets of angle measures can form a triangle?

Select all that apply:

- 50, 50, 50
- 25, 25, 40
- 55, 25, 100
- 35, 45, 95
- 40, 55, 85

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]

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