Answer:
55, Acute angled scalene triangle
90, Right angled scalene triangle
105, Obtuse angled scalene triangle
Step-by-step explanation:
Let us learn the property of a triangle.
Let a triangle be [tex]\triangle ABC[/tex].
Sum of all the three internal angles of a triangle is always equal to [tex]180^\circ[/tex].
OR
[tex]\angle A+\angle B+\angle C=180^\circ[/tex]
Given that triangles have 2 angles. Let us suppose, the third angle be [tex]x^\circ[/tex]
1. Triangle 1: two angles are [tex]50^\circ, 75^\circ[/tex]
[tex]\therefore 50^\circ+75^\circ+x=180^\circ\\\Rightarrow 125+x=180^\circ\\\Rightarrow x=55^\circ[/tex]
All the angles are less than 90 and no two angles are equal so, it is acute angle scalene triangle. (No sides equal)
2. Triangle 1: two angles are [tex]60^\circ, 30^\circ[/tex]
[tex]\therefore 60^\circ+30^\circ+x=180^\circ\\\Rightarrow 90+x=180^\circ\\\Rightarrow x=90^\circ[/tex]
One angle is 90 and not two angles are equal so, right angled scalene triangle.(No sides equal)
3. Triangle 1: two angles are [tex]30^\circ, 45^\circ[/tex]
[tex]\therefore 30^\circ+45^\circ+x=180^\circ\\\Rightarrow 75+x=180^\circ\\\Rightarrow x=105^\circ[/tex]
One angle is more than 90 and not two angles are equal so, obtuse angled scalene triangle.(No sides equal)
So, the answers are:
55, Acute angled scalene triangle
90, Right angled scalene triangle
105, Obtuse angled scalene triangle
