Answer:
Angles measuring 90°, 45°, and 45°: Can make triangle
Angles measuring 27°, 35°, and 108°: Can not make triangle
Angles measuring 82°, 41°, and 57°: Can make triangle
Sides measuring 8 cm, 12 cm, and 5 cm: Can make triangle
Sides measuring 7 in., 4 in., and 13 in: Can not make triangle
Sides measuring 43 cm, 41 cm, and 58 cm: Can make triangle
Step-by-step explanation:
For the angles to form a triangle, there sum must be equal to 180°
<u>Angles measuring 90°, 45°, and 45°</u>
Sum of Angles = 90° + 45° +45° = 180°
Hence, this combination can make triangle.
<u>Angles measuring 27°, 35°, and 108°</u>
Sum of Angles = 27° + 35° + 108° = 170° ≠ 180°
Hence, this combination can not make triangle.
<u>Angles measuring 82°, 41°, and 57°</u>
Sum of Angles = 82° + 41° +57° = 180°
Hence, this combination can make triangle.
For three sides to form a triangle the sum of the two sides must be greater than the length of third side.
<u>Sides measuring 8 cm, 12 cm, and 5 cm</u>
(8 cm + 12 cm) > 5 cm (True)
(8 cm + 5 cm) > 12 cm (True)
(12 cm + 5 cm) > 8 cm (True)
Hence, this combination can make triangle.
<u>Sides measuring 7 in., 4 in., and 13 in</u>
(7 in + 4 in) > 13 in (False)
Hence, this combination can not make triangle.
<u>Sides measuring 43 cm, 41 cm, and 58 cm</u>
(43 cm + 41 cm) > 58 cm (True)
(43 cm + 58 cm) > 41 cm (True)
(41 cm + 58 cm) > 43 cm (True)
Hence, this combination can make triangle.
