Question

Can someone help me with this

Which of the following combinations would result in multiple triangles? SHOW WORK

A: 45 degrees, 82 degrees, 53 degrees

B: 5 degrees, 122 degrees, 61 degrees

C: 2 cm, 8 cm, 10 cm

D: 10 in, 20 in, 75 degrees

Answer 1

Answer: Options 2 and 4

Explanation:

Option 1: The angles add to
`180^(\circ)`, so the angles can form a triangle. However, because there are no side lengths, the triangle is only defined up to similarity.

Option 2: The angles do not add to
`180^(\circ)`, so a triangle cannot be formed.

Option 3: The side lengths do not satisfy the triangle inequality, so a triangle cannot be formed.

Option 4: It is not specified what side the
`75^(\circ)` is opposite of, so multiple triangles can be formed.