Question

Geometry help?

Answer 1

`x=16 2/3`

Explanation:

`triangleMOP` is similar to `triangleMLN` because all the angles of both triangles are equal.
This means that the ratio of two sides in one triangle will be same as that of another triangle so `"MO"/"MP"="ML"/"MN"`
After putting in values, we get `x/15=(x+20)/(15+18`

`x/15=(x+20)/33`

`33x=15x+300`

`18x=300`

`x=16 2/3`

Answer 2

`C`

Explanation:

We can use the Side-Splitter Theorem to solve this problem. It states:

• If a line is parallel to a side of a triangle and intersect the other two sides, then this line divides those two sides proportionally.

Since `OP` || `LN`, this theorem applies.

So we can set up this proportion:
`x/20 = 15/18`

Now cross multiply and solve:
`x/20 = 15/18`

`x xx 18 = 20 xx 15`

`18x = 300`

`x = 300/18 rarr 16 12/18 rarr 16 2/3`

So the answer is `C`

Answer 3

Answer: `x=16*2/3`

Explanation:

Since `OP` is parallel to `LN`, we know that `angleMOP=angleMLN` and `angleMPO=angleMNL` from the Corresponding Angles Theorem

Further, we also have that `angleOMP=angleLMN` since they are the same angle.

Therefore `triangleOMP` is similar to `triangleLMN` (`triangleOMP~triangleLMN`)

Since similar triangles have the same side length ratio:
`(MO)/(ML)=(MP)/(MN)`

Plugging numbers in, we have:
`x/(x+20)=15/(15+18)`

We can now solve this equation by cross multiplication:
`33x=15(x+20)`
`33x=15x+300`
`18x=300`
`x=16*2/3`