Question

1. Find angle measures and use angles to classify triangles.

Answer 1

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 $\triangle ABC$.

Sum of all the three internal angles of a triangle is always equal to $180^\circ$.

OR

$\angle A+\angle B+\angle C=180^\circ$

Given that triangles have 2 angles. Let us suppose, the third angle be $x^\circ$

1. Triangle 1: two angles are $50^\circ, 75^\circ$

$\therefore 50^\circ+75^\circ+x=180^\circ\\\Rightarrow 125+x=180^\circ\\\Rightarrow x=55^\circ$

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 $60^\circ, 30^\circ$

$\therefore 60^\circ+30^\circ+x=180^\circ\\\Rightarrow 90+x=180^\circ\\\Rightarrow x=90^\circ$

One angle is 90 and not two angles are equal so, right angled scalene triangle.(No sides equal)

3. Triangle 1: two angles are $30^\circ, 45^\circ$

$\therefore 30^\circ+45^\circ+x=180^\circ\\\Rightarrow 75+x=180^\circ\\\Rightarrow x=105^\circ$

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