A triangle is a plane shape with three straight sides. There are different types of triangles. Thus the required answers are:
1. Option B. One
2. Option B. More than one
3. Option B. More than one
4. Option A. None
Triangles are shapes bounded by three straight sides, so that the sum of its internal angles is [tex]180^{o}[/tex]. Triangles has two classes, viz: classification according to length of sides, and classification according to measure of angles.
Types of triangles classified with respect to the length of sides are: isosceles, equilateral and scalene. Whiles the types classified with respect to the measure of angles are: right angled, obtuse angled and acute angled.
Therefore, the answers to the given question are:
1. The number of triangles that can be constructed when given 3 angles (e.g 10º, 80º, and 90º) is one. So that option B, One, is appropriate.
2. The number of triangles that can be constructed when given the length of its sides (e.g 15 cm, 7 cm, and 5 cm) is greater than one. Thus, option B, more than one, is appropriate.
3. The number of triangles that can be constructed when given the length of its sides (e.g 1 m, 2 m, and 2 m) is greater than one. Thus, option B, more than one, is appropriate.
4. Given that the measure of each angle is 63°, then no triangle can be constructed. This is because:
63° + 63° + 63° ≠ [tex]180^{o}[/tex]
Thus the answer is option A. none
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