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This john what we notice is we have three angles all right now. We know know that there is a relationship between these two angles right those are both interior and theyre both on the same side therefore. We call those alexander.
Do you remember when theyre on the same side. Theyre both interior. No zack you remember what happens when theyre both interior on the same side of the transversal.
We call them consecutive interior. But heres the problem remember. Consecutive interior angles are supplementary meaning they add up to 180.
So if i was to write an equation for this i would have 8x minus 10. Plus. 6y plus.
20. Equals. 180.
The problem. With that is i have two variables and only one equation when you guys talk about systems of equations when we have two variables we have to have two different equations so even though that is a good angle relationship since we have two different variables. We cant solve it that way so what were going to do is say all right well.
How about then lets just deal with the angles. With the xs forget about the angle. With the wife right.
Now lets just deal with the angles of the xs so sierra do you know how these two angles. Relate to each other are they interior exterior interior between the parallel lines all right and all right so the interior on the table eyes are on the same side or alternating sides all three and so we call them alternate interior angles. And we know alternate area angles.
How do they relate to each other theyre equal and measure right so therefore we can set up an equation 8x minus. 10. Equals 7x and please ladies joanne lets get in the habit.
If you apply a theorem lets write it down alternate interior. Right i decided that those two angles are equal to each other because i know alternate interior angles are equal in value when we have parallel lines.
So i forgot to add that on the figure right the figure had parallel lines. If theyre only equal and measure. When you have pair of lines.
So now lets go ahead and solve okay so now i get x equals. 10. All right so now ladies and gentlemen.
I can figure out the value for each one of these so if i say x equals. 10. I could say 8.
Times 10. Minus 10 equals that angle. And then i have 7 times.
10. Well. Thats going to equal 70.
And that equals 70 right so therefore these two angles instead of using equations. Im now going to write in their value. So thats 70 degrees.
And thats 70 degrees. Does everybody agree with what i did i just took the value of x plugged it into those equations to find my now measure of my angle. Now the last thing i need to do is determine how does 6y and 20 relate to 70 blake do you have any idea.
How are these two angles related theyre not on parallel lines. Theyre just on a line. But theyre being cut by transversal but they make up a what what are these two angles.
When you add them up make up they make up a line. So therefore we call them supplementary right and theyre also a adjacent since theyre adjacent and supplementary another vocabulary word is a linear pair a linear pair again is supplement so then last one ladies john i know that this times. This adds up to 180.
So 6y plus 20. Plus.
70. Degrees. Equals 180.
Degrees. All right. So.
Now. We can just go. Ahead.
And solve. So. Its become six y equals.
90. Im sorry six y plus. 90.
Equals. 180. Subtract 90.
Degrees. So. Therefore.
I have six. Y equals. 90.
And therefore divided by six y equals. So there you go. We figured out what the value of x.
Was and we figure out the value of y. Was by using our relationship for parallel lines and also remembering supplementary angles. Which you guys cannot forget right whenever two angles make up a line thats youre gonna have supplementary angles.
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