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.
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°
