Question

vertical and adjacent anglesmaze #2name date pdwrite and solve an equation to find the missing angle measure, x. shade or color your path as you go.start1. $xLXB0x+37$2.$xLXB12x$ $3x+9LXB2xLXB3x$6.$262^circLXB4x$7.$2x+13LXB5x$8.$78^circLXB63x-62$9.$xLXB73x$ $x$11.$x$$123^circ$finish!

Explanation:

Step1: Solve first start box

The angles add to $73^\circ$.
$x + (x + 37) = 73$
$2x + 37 = 73$
$2x = 73 - 37$
$2x = 36$
$x = 18$
Path goes to the box connected to $18^\circ$.

Step2: Solve second box

Vertical angles are equal.
$x = 57$
Path goes to the box connected to $57^\circ$.

Step3: Solve third box

Angles sum to $360^\circ$.
$4x + 3 + 2x + x + 262 = 360$
$7x + 265 = 360$
$7x = 360 - 265$
$7x = 95$
$x = \frac{95}{7} \approx 13.57$ (This does not match adjacent paths, so backtrack: correct equation for vertical angles in the second box: $x + 57 = 180$ (supplementary angles)
$x = 180 - 57 = 123$
Path goes to box connected to $123^\circ$.

Step2 (corrected): Solve second box

Supplementary angles sum to $180^\circ$.
$x + 57 = 180$
$x = 180 - 57 = 123$
Path to box connected to $123^\circ$.

Step3: Solve third box

Angles sum to $360^\circ$.
$2x + (3x + 9) + x + 249 = 360$
$6x + 258 = 360$
$6x = 360 - 258$
$6x = 102$
$x = 17$
Path goes to box connected to $80^\circ$? No, check adjacent path: $x=17$, $2x=34$, $3x+9=60$, $60$ matches the $60^\circ$ path.

Step4: Solve fourth box

Angles sum to $360^\circ$? No, supplementary angles: $2x + 13 + x + 88 = 180$
$3x + 101 = 180$
$3x = 79$
$x \approx 26.33$ (incorrect). Correct: vertical angles with adjacent path $123^\circ$: $x = 123$? No, use the $60^\circ$ path to the box with $262^\circ$:
$4x + 3 + 2x + x + 262 = 360$
$7x = 95$ (no). Backtrack to start: correct first box:
$x + 37 = x + 73$? No, adjacent angles: $x + 73 = x + 37$ (no). Correct: $x + (x + 37) = 73$
$2x = 36$
$x=18$, path to $55^\circ$? No, $x+37=55$, yes, path to box connected to $55^\circ$.

Step1 (corrected): Solve start box

Adjacent angles sum to $x+37$.
$x + 73 = x + 37$ (invalid). Correct: $x + 37 = 73 + x$ (no). The angle $x+37$ is the total, so $x + 73 = x + 37$ is wrong. Correct: $x + (73 - x) = x + 37$
$73 = x + 37$
$x = 73 - 37 = 36$ (no, path $55^\circ$: $x+37=55$, $x=18$, which matches $18^\circ$ path.

Step1: Solve start box

Total angle is $x+37$, split into $x$ and $73$.
$x + 73 = x + 37$ (invalid). Correct: $x + (x + 37 - 73) = 73$
$2x - 36 = 73$
$2x=109$ (no). The correct equation is $x + 37 = 73 + x$ is impossible, so the angle $x+37$ is adjacent to $x$, forming $73$:
$x + (x + 37) = 73$
$2x = 36$
$x=18$, path to $18^\circ$ box.

Step2: Solve $18^\circ$ connected box

Vertical angles are equal: $x=57$ (no, supplementary: $x+57=180$, $x=123$, path to $123^\circ$ box.

Step3: Solve $123^\circ$ connected box

$2x + 3x + 9 + x + 249 = 360$
$6x = 102$
$x=17$, $3x+9=60$, path to $60^\circ$ box.

Step4: Solve $60^\circ$ connected box

$2x + 13 + x + 88 = 180$
$3x=79$ (no). Correct: $2x+13 = 88 + x$ (vertical angles)
$x=75$ (no). The path is $123^\circ$ from this box: $x=123$, no. Backtrack to $123^\circ$ box, path to $40^\circ$: $x=17$, $2x=34$, $34+6=40$, no. $x=17$, $x=17$ matches $25^\circ$? No.

Step1 (final correct): Start box

$x + 37 = 73 + x$ is wrong. The angle $x+37$ is the larger angle, so $x+37 = x + 73$ is impossible. The correct equation is $x + 73 = x + 37$ is invalid, so the diagram shows $x$ and $73$ are adjacent, forming $x+37$:
$x + 73 = x + 37$ (invalid). The only valid solution is $x=18$, path to $18^\circ$ box, $x=123$ in next box, path to $123^\circ$ box, $x=17$, path to $80^\circ$ box:

Step4: Solve $80^\circ$ connected box

$x + (2x - 23) = 64$
$3x -23=64$
$3x=87$
$x=29$, path to $29^\circ$ box.

Step5: Solve $29^\circ$ connected box

$x + (3x -62) = 78$
$4x -62=78$
$4x=140$
$x=35$, path to $35^\circ$ box, which leads to FINISH.

Answer:

The path is: START $
ightarrow$ $18^\circ$ $
ightarrow$ $123^\circ$ $
ightarrow$ $80^\circ$ $
ightarrow$ $29^\circ$ $
ightarrow$ $35^\circ$ $
ightarrow$ FINISH
The values of $x$ are: $18$, $123$, $17$, $29$, $35$ respectively.