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!
ANSWER
The smaller angle is

.EXPLANATION
Let the angles be

where y is the smaller angle.
Since they are supplementary, they will add up to 180°.
This implies that,

If one angle is 4 times the other, we can then write the following equation,

We put equation (2) into equation (1) to get,


We divide through by 5 to obtain,

This implies that,

Hey!
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Solution:
9 + 22 = x + 1
9 + 22 - x = x + 1 - x
31 - x = 1
31 - x 31 = 31 - 1
x = 30
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Answer:
x = 30
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Hope This Helped! Good Luck!
5=3(-2) +b
5=(-6)+b
+6 +6
11=b