Explanation:
(I'll be adding more answers to this answer soon!)
Alright, let's start off with the first question. :)
So, the entire length of AC is 60.
AB + BC = AC, as you can infer from the diagram.
We know that AB is 2x + 8, and AC is 3x + 7.
So,
2x + 8 + 3x + 7 = 60.
Now, we can simply evaluate for x:
Combine the like terms to get 5x + 15 = 60
Subtract 15 to get 5x = 45
Divide by 5 to get the first question's answer as x = 5 :)
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Time for the second question!
AD is a straight angle. If an angle is straight, it measures 180 degrees. So,
AD = 180
From the diagram, we can tell that x+17 and 5x+13 add up to 180.
x + 17 + 5x + 13 = 180
Now, we can simply solve for x!
6x + 30 = 180
6x = 180 - 30 = 150
x = 150 / 6 = 25
So, we get x = 25 as the answer to the second question! :)