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Timmeh
Hi Bre,

Since lines a and b are parallel, we know that in the image:
- ∡1 ⇔ ∡5
- ∡2 ⇔ ∡6
-       ...
- ∡4 ⇔ ∡8

We're given the angle of ∡7, which is 114°.  We can see that ∡7 + ∡8 will equal to 180° (since line b is a straight line) and since ∡8 ⇔ ∡4, we can deduct that ∡7 + ∡4 = 180°.

From here, it's just imputing the information and solving.
⇒ 114° + ∡4 = 180°
⇒ ∡4 = 180° - 114°
⇒ ∡4 = 66°

-Hope this helps!
vinhelson
The measure of angle 4 is 66 degrees. That is because the angle of 4 is equivalent to the angle of 8 because of the parallel lines. A straight line is 180 degrees so 180 - 114 = 66 degrees. Angles 7 and 8 have to equal 180.

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