Final answer:
The number of triangles that can be constructed with given angles and sides.
Step-by-step explanation:
The sum of the angles in a triangle is always 180 degrees. For the first question, the given angles are 10º, 80º, and 90º. Since their sum is 180º, it is possible to construct one triangle with these angles.
For the second question, the given sides are 15 cm, 7 cm, and 5 cm. To determine if a triangle can be constructed, we can use the triangle inequality theorem: the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side. Using this rule, we can see that 7+5=12, which is less than 15. Therefore, it is not possible to construct a triangle with these sides.
For the third question, the given sides are 1 m, 2 m, and 2 m. Again, using the triangle inequality theorem, we can see that 1+2=3, which is less than 2. Therefore, it is not possible to construct a triangle with these sides.
For the fourth question, the given angles are all 63°. Since the sum of the angles in a triangle is always 180°, no triangle can be constructed with three angles measuring 63°.