Question

Please help me with this question, I don’t understand?

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Answer 1

`30^@` and `150^@`

Explanation:

The question is in the context of a line cutting across two parallel lines, resulting in eight angles, which are four of one size and four of another size, those two distinct sizes adding up to `pi` radians a.k.a. `180^@`. That is: they are supplementary angles.

So we are looking for `theta` such that `theta + 5 theta = 180^@`

Hence `theta = 30^@` or `pi/6` radians.

So the two angles are `30^@` and `150^@` or `pi/6` and `(5pi)/6` radians.

Answer 2

30 and 150 degrees

Explanation:

When a parallel line is cut by a transverse line, all the angles formed can be divided into two parts - i) the exterior angle and ii) the interior angle.

The interior angles are those which lie between the parallel lines and the exterior angles are those which lie outside of parallel lines.

the question says the angles are on same side and then it can be either interior or exterior angles.

Also, same side angles are supplementary angles (the sum of which adds to 180 degrees because the parallel lines are straight which has 180 degrees.

Let , the first angle be `x` and the other angle be `x/5` (because the second angle is 5 times smaller than the first angle, so we divide the first angle `x` by 5.

Therefore, `x + x/5 =180`
which is, `(5x+x)/5 = 180`
or, `5x+x = 180xx 5`

or, `6x = 180 xx 5`

or, `x = (180 xx 5)/6`

or, `x = (cancel (180) 30 xx 5)/ (cancel (6)1)` = `150`

Now the other angle is `x/5`, which is `150/5` = 30

Another way to find the other angle would be that after knowing the first angle (which is 150), subtract it from 180 (because sum of both angles is 180) and we will get 30 as the other angle.