Answer:
Hello!!! Princess Sakura here ^^
Step-by-step explanation:
First we will go find the angle measure of 3.
We already know that <1 & <2 are 55° & 60°.
Tip: The sum of all the angles in a triangle is 180°.
So now if we add those two angles we'd get 115°, then we could subtract it from 180 to get the measure of <3, which is 65°.
For <4 it should be easier if you know that line AB is parallel to line CD and then line AC is the transversal because it goes through both lines.
Tip: Alternate interiors are angles that are equal to each other.
Then when you know all this you can figure out that <2 and <4 are alternate interiors which makes them equal to each other. So if they said that <2 is 60° then it'll only make sense if <4 is also 60°.
Now for <5 we know that <3,<4, and <5 are all on a line so that makes the sum of those three angles 180°.
So we would do the sum of <3, <4, then x and all that is equal to 180°.
[tex]65+60+x=180\\125+x=180\\x=55[/tex]
Great now we know <5 is 55°.
We will now move on to <6. It has the same relationship to <4 as <2 and <4. So if <4 is 60° that means <6 has to be 60°° as well.
Tip: The sum of these two angles (in this case are <5 and <6) are equal to t the outer angle (<7)
Now we have to figure out the measure of <7. First we have to notice that if we add <5 and <6 we will get <7. So 55 + 60 = 115 and that's it <7 is 115°.
Now the recap:
<3=65°
<4=60°
<5=55°
<6=60°
<7=115°
