Question

Which angle or side combinations can make a triangle? Select all that apply. Angles measuring 90°, 45°, and 45°. Angles measuring 27°, 35°, and 108°. Angles measuring 82°, 41°, and 57°. Sides measuring 8 cm, 12 cm, and 5 cm. Sides measuring 7 in., 4 in., and 13 in. Sides measuring 43 cm, 41 cm, and 58 cm.

Answer 1

A- Angles measuring 90°, 45°, and 45°.

C- Angles measuring 82°, 41°, and 57°.

D- Sides measuring 8 cm, 12 cm, and 5 cm

F- Sides measuring 43 cm, 41 cm, and 58 cm.

Explanation:

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Answer 2

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

Explanation:

For the angles to form a triangle, there sum must be equal to 180°

Angles measuring 90°, 45°, and 45°

Sum of Angles = 90° + 45° +45° = 180°

Hence, this combination can make triangle.

Angles measuring 27°, 35°, and 108°

Sum of Angles = 27° + 35° + 108° = 170° ≠ 180°

Hence, this combination can not make triangle.

Angles measuring 82°, 41°, and 57°

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.

Sides measuring 8 cm, 12 cm, and 5 cm

(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.

Sides measuring 7 in., 4 in., and 13 in

(7 in + 4 in) > 13 in (False)

Hence, this combination can not make triangle.

Sides measuring 43 cm, 41 cm, and 58 cm

(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.