I am stuck...Please Help!

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snow123

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Sep 25, 2010
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Hi,
I don't know where to post this, so I hope I picked the right category.
I am attaching the question from my textbook. I don't know how to figure out what x, y and z are. Please help me.
Thank you.
 


Start by finding the measure of the third angle, within the inner triangle; the other two angles are 40 degrees and 80 degrees.

 
ok so the measure of the third angle, within the inner triangle is 60 degrees...now what do I do?
 


Next, use the properties concerning "equal opposite angles" when a transversal (i.e., a slanted line) intersects two parallel lines, to find additional angles, in the given diagram.

Hold on. I'm scanning an quick sketch.

 
snow123 said:
Hi,
I don't know where to post this, so I hope I picked the right category.
I am attaching the question from my textbook. I don't know how to figure out what x, y and z are. Please help me.
Thank you.
Click to expand...

You've found the measure of the third angle of the "inner" triangle as suggested.

Now, you probably want to use this theorem:

If a segment joins the midpoints of two sides of a triangle, it is parallel to the third side and equal to half the length of the third side.

You've got THREE segments joining the midpoints of sides of the largest triangle. So, you have three sets of parallel lines...that should give you a good start!
 


(Double-click to expand image, if needed.)

[attachment=0:3vrqhxdt]Transveral.jpg[/attachment:3vrqhxdt]

Think of the letter Z.

Do you see the letter Z, in the portion of your diagram which I drew with some lines extended.

Those "inner" angles in the letter Z (labeled as 60 degrees) are called somelike like the" inner opposite angles" that arise when a diagonal line (transversal) passes through two parallel lines.

The "outer opposite angles" are equal, too.

You can look it up in your textbook, or google, for more detailed illustrations.

Use these opposite-angle properties, to find enough angles to determine x, y, and z.

 
Mrspi said:
If a segment joins the midpoints of two sides of a triangle, it is parallel to the third side
Click to expand...

Yes, this is important to remember, to apply what I posted above to other pairs of parallel lines extended (with their respective transversal) within the given diagram.

I probably should have mentioned this, too.

 
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