A diagonal walkway cuts through a park bordered by two parallel streets. The parks department plans to add an additional walkway as indicated by the dashed line segment in the figure.
Question 15 options:
A)
42
B)
48
C)
90
D)
138

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##### 1 Attachment

- mathstudent55

Is the question what is the measure of x?

- anonymous

i have no clue....

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## More answers

- mathstudent55

That is all the question states? The problem does not ask a question.

- ali2x2

im stuck...

- anonymous

exactly.... and yes that's the full question

- mathstudent55

Since I see an x in the figure, I'll assume the question is "what is the measure of the angle labeled x?"

- mathstudent55

Ok, here it is:
The streets are parallel.
Do you know about alternate interior angles?

- anonymous

maybe... I'll be honest, we never learned how to do this. and yes.

- mathstudent55

Using parallel lines and a transversal, and alternate interior angles, what is the measure of angle a?
|dw:1438109253345:dw|

- anonymous

it would be 132

- mathstudent55

Yes. Let's write that.
|dw:1438109440040:dw|

- mathstudent55

Using the figure above, can you find the measure of angle b?

- mathstudent55

What is the relationship between angles a and b?

- anonymous

48 =b

- anonymous

180-132=48

- mathstudent55

Great.
a and b are a linear pair. They are supplementary, so a + b = 180, and a = 132, so b = 148. Good.

- mathstudent55

|dw:1438109607854:dw|

- mathstudent55

Now can you find the measure of the angle labeled x?

- anonymous

so adding 90 and 48? gives me 42

- mathstudent55

Actually, subtracting 48 from 90 gives you x = 42.
90 + x + 48 = 180
x + 48 = 90
x = 90 - 48 <------ subtract 48 from 90
x = 42
You are correct.

- anonymous

oh then i did it the longer way but it still works. thank you!

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