Can someone please explain to me how to find missing angles in geometry?

[Taxi]

I was taking a quiz, and I had no idea how to find some of the missing angles. I know how to do basic problems finding angles, but it's really challenging to do a problem that involves finding multiple angles one-by-one. Can someone please show me an example of how to find missing angles from a set of many lines? I would really appreciate it ;;

[Peanutbutter Cat]

If you mean missing angles are you talking about something like this?



So let's say that:
Angle 8 is 132 degrees and that's all we're given. We can solve for every single angle here now.

So there are a couple of rules here, the two lines that are being intersected are exactly parallel, so we can say that...

1. Angle 7 and Angle 6 are both the angle values of 8 - 180. so we can say 180 - 132 = 48. Therefore both Angle 7 and Angle 6 are 48 degrees. Angles that are right beside each other are supplementary (that angle - 180 degrees). This is because if you were to look at a 180 degree angle, it is a completely flat line, and angles right next to each other divide that line into two parts.

2. Next, we could definitely use the previous rule for angle 5, by saying 48 - 180. However, if you were to do this you would find that Angle 5 is congruent to Angle 8. Angles across from each other, given this format, are congruent to each other. This means that Angle 5 is also 132 degrees. This same logic can be applied with Angle 6 and Angle 7

3. The final rule is how we get the other side of this problem (Angles 1 2 3 and 4.) Because the intersecting line is a straight line, and both lines are parallel, each line is being intersected in the exact same way. So we can just match each angle up.
Angle 8 = Angle 4; Angle 7 = Angle 3; and so on. So, if you have solved one side of this problem, you have solved the other.


And if you understand this logic, you can apply this to much more complex scenarios. all you have to do is look at each 'cluster' of angles created by any intersecting line between any number of parallels the same as the example above.

[Taxi]

If you mean missing angles are you talking about something like this?



So let's say that:
Angle 8 is 132 degrees and that's all we're given. We can solve for every single angle here now.

So there are a couple of rules here, the two lines that are being intersected are exactly parallel, so we can say that...

1. Angle 7 and Angle 6 are both the angle values of 8 - 180. so we can say 180 - 132 = 48. Therefore both Angle 7 and Angle 6 are 48 degrees. Angles that are right beside each other are supplementary (that angle - 180 degrees). This is because if you were to look at a 180 degree angle, it is a completely flat line, and angles right next to each other divide that line into two parts.

2. Next, we could definitely use the previous rule for angle 5, by saying 48 - 180. However, if you were to do this you would find that Angle 5 is congruent to Angle 8. Angles across from each other, given this format, are congruent to each other. This means that Angle 5 is also 132 degrees. This same logic can be applied with Angle 6 and Angle 7

3. The final rule is how we get the other side of this problem (Angles 1 2 3 and 4.) Because the intersecting line is a straight line, and both lines are parallel, each line is being intersected in the exact same way. So we can just match each angle up.
Angle 8 = Angle 4; Angle 7 = Angle 3; and so on. So, if you have solved one side of this problem, you have solved the other.


And if you understand this logic, you can apply this to much more complex scenarios. all you have to do is look at each 'cluster' of angles created by any intersecting line between any number of parallels the same as the example above.

Oh my gosh you saved me! Thank you so much!!!