find the value of the variable.
17. diagram: two intersecting lines with angles 110° and (2x + 40)°
18. diagram: two intersecting lines with angles x° and (5x − 48)°
19. diagram: two intersecting lines with angles 64° and (48 + x)°
20. diagram: a horizontal line intersected by another line, with angles 75° and (2x − 5)°
21. diagram: a horizontal line intersected by another line, with angles (3x + 8)° and x°
22. diagram: a horizontal line intersected by another line, with angles (2x + 8)° and (3x + 17)°

Question

Accepted Answer

### Problem 17
# Explanation:
## Step1: Vertical angles are equal
$2x + 40 = 110$
## Step2: Solve for x
$2x = 110 - 40$
$2x = 70$
$x = \frac{70}{2}$
$x = 35$
# Answer: 35

### Problem 18
# Explanation:
## Step1: Vertical angles are equal
$x = 5x - 48$
## Step2: Solve for x
$48 = 5x - x$
$48 = 4x$
$x = \frac{48}{4}$
$x = 12$
# Answer: 12

### Problem 19
# Explanation:
## Step1: Vertical angles are equal
$48 + x = 64$
## Step2: Solve for x
$x = 64 - 48$
$x = 16$
# Answer: 16

### Problem 20
# Explanation:
## Step1: Angles on a straight line sum to 180°
$75 + (2x - 5) = 180$
## Step2: Simplify and solve for x
$75 + 2x - 5 = 180$
$2x + 70 = 180$
$2x = 180 - 70$
$2x = 110$
$x = \frac{110}{2}$
$x = 55$
# Answer: 55

### Problem 21
# Explanation:
## Step1: Vertical angles are equal, and linear pair sums to 180° (or vertical angles: $x = 3x + 8$? Wait, no—wait, the angle $x$ and $(3x + 8)$: wait, actually, $x$ and $(3x + 8)$ are supplementary? Wait, no, looking at the diagram: the two angles are vertical? Wait, no, the straight line and the transversal: the angle $x$ and $(3x + 8)$—wait, no, actually, $x$ and $(3x + 8)$ are supplementary? Wait, no, let's re-examine. Wait, the angle $x$ and $(3x + 8)$: if they are adjacent and form a linear pair? Wait, no, the diagram shows a straight line and a transversal, so the angle $x$ and $(3x + 8)$—wait, no, actually, $x$ and $(3x + 8)$ are vertical? Wait, no, maybe I misread. Wait, the problem is: the angle $x$ and $(3x + 8)$—wait, no, the correct approach: vertical angles are equal, and linear pairs sum to 180. Wait, in the diagram, the angle $x$ and the angle opposite to $(3x + 8)$? Wait, no, let's see: the straight line, and the transversal creates two angles: $x$ and $(3x + 8)$. Wait, actually, $x$ and $(3x + 8)$ are supplementary? Wait, no, maybe $x$ and $(3x + 8)$ are vertical? Wait, no, perhaps the angle $x$ and $(3x + 8)$ are adjacent and form a linear pair? Wait, no, let's do the math. Wait, the correct equation: since they are vertical angles? No, wait, the angle $x$ and $(3x + 8)$—wait, maybe the angle $x$ is equal to the vertical angle of $(3x + 8)$? No, wait, let's think again. Wait, the problem is: the angle $x$ and $(3x + 8)$—wait, maybe the sum of $x$ and $(3x + 8)$ is 180? No, that can't be. Wait, no, the correct approach: vertical angles are equal, so $x = 3x + 8$? No, that would give negative x. Wait, no, maybe the angle $x$ and $(3x + 8)$ are supplementary? Wait, no, let's check the diagram again. Wait, the straight line, and the transversal: the angle $x$ and $(3x + 8)$—wait, maybe the angle $x$ is equal to the angle adjacent to $(3x + 8)$? Wait, no, perhaps I made a mistake. Wait, let's re-express: the angle $x$ and $(3x + 8)$ are vertical angles? No, vertical angles are equal. Wait, if $x$ and $(3x + 8)$ are vertical, then $x = 3x + 8$ → $-2x = 8$ → $x = -4$, which is impossible. So maybe they are supplementary? So $x + (3x + 8) = 180$ → $4x + 8 = 180$ → $4x = 172$ → $x = 43$. Wait, that makes sense. So:
## Step1: Supplementary angles sum to 180°
$x + (3x + 8) = 180$
## Step2: Solve for x
$4x + 8 = 180$
$4x = 180 - 8$
$4x = 172$
$x = \frac{172}{4}$
$x = 43$
# Answer: 43

### Problem 22
# Explanation:
## Step1: Supplementary angles sum to 180°
$(2x + 8) + (3x + 17) = 180$
## Step2: Solve for x
$5x + 25 = 180$
$5x = 180 - 25$
$5x = 155$
$x = \frac{155}{5}$
$x = 31$
# Answer: 31

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QUESTION IMAGE

Question

Explanation:

Problem 17

Step1: Vertical angles are equal

Step2: Solve for x

Step1: Vertical angles are equal

Step2: Solve for x

Step1: Vertical angles are equal

Step2: Solve for x

Answer:

Problem 18