Question

Given a||b and c is not parallel to a or b, which statements must be true?

1) 1/2
2) 3/4
3) 5/6
4) 7/8

Answer 1

In this scenario, where a || b and c is not parallel to a or b, the angle between c and a or b is 90 degrees, and the remaining angle between a and b is also 90 degrees, ensuring that the sum of the angles is 180 degrees.Thus,the correct option is 3) 5/6

Step-by-step explanation:

In the given scenario where
`\(a \parallel b\)` and (c) is not parallel to (a) or (b), the statement that must be true is 3) (5/6). To understand why, let's consider the possibilities for the angles formed by the lines (a), (b), and (c).

If (a) and (b) are parallel, corresponding angles are equal, and if \(c\) is not parallel to (a) or (b), it means that (c) intersects (a) and (b) at distinct points. In this case, the angle formed by (c) and (a) or (b) must be different from the corresponding angles between (a) and (b).

Now, consider the sum of angles formed by (a), (b), and (c). It is well-known that the sum of angles in a triangle is
`\(180^\circ\)`. Therefore, if
`\(a \parallel b\)` and (c) is not parallel to (a) or (b), the angle between (c) and (a) or (b) must be
`\(90^\circ\)`, leaving the other angle between (a) and (b) as
`\(90^\circ\)` as well.

So, the correct statement is (5/6) because the angle between (c) and (a) or (b) is
`\(90^\circ\)`, and the remaining angle between (a) and (b) is also
`\(90^\circ\)`, ensuring that the sum of the angles is
`\(180^\circ\)`.

Therefore,the correct option is 3) 5/6