Joseph, I hope I can still help.
We know that supplementary angles add up to 180 degrees, and complementary angles add up to 90 degrees, right?
If we know the measure of one angle and ask for its complement, then we subtract that angle's measure from 90. To get it's supplement, we subtract from 180.
If we let x = the measure of our angle, then the supplement is 180 - x and the compliment is 90 - x.
Since we have that the supplement is 30 more than 4 times the complement, then 180 - x = 4(90 - x) + 30. We have to multiply the compliment by 4 and then add 30 to it to get the supplement.
180 - x = 4(90 - x) + 30. What do we do first? Distribute!
180 - x = 4(90) + 4(-x) + 30
180 - x = 360 - 4x + 30
Combining like terms on the left, we get 180 - x = 390 - 4x
Adding 4x to both sides, we get 180 + 3x = 390
Subtracting 180 from both sides, we get 3x = 210
Dividing both sides by 3, we get x = 70.
Let's check.
180 - 70 = 4(90 - 70) + 30
110 = 360 - 280 + 30
110 = 110
Check!
Hope this helps!
