(10 points) when given the m∠1 =(2x - 9) and m∠2 = (5x - 7),find the value of x that will make m || n?

For this one, set bot angles equal to 180 like this:  

2x-9+5x-7=180

The reasoning is a straight line has an angle of 180 and the two angles being in opposite positions, you can set them equal to 180.

Now combine like terms:

2x+5x=7x

-9-7=-16

Now your new problem looks like:

7x-16=180

Next isolate the x:

7x-16+16=180+16

7x=196

Now divide by 7 to make the x by itself:

7x/7=196/7

This comes out even to x=28.

Now since it is a word problem, higher math says to answer it in the same format:

To make m and n congruent, x has to equal 28.

Hope this helps!