Question

find the value of each variable.
10.
11.
12.

Explanation:

Step1: Sum of exterior angles = 360°

$2x + 3x + 4x + x = 360$

Step2: Combine like terms

$10x = 360$

Step3: Solve for $x$

$x = \frac{360}{10} = 36$

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Step1: Find sum of interior angles (8 sides)

Sum = $(8-2)\times180 = 1080^\circ$

Step2: Set up angle sum equation

$n + 161 + (n-12) + (n+30) + n + 134 + (n+16) + 126 = 1080$

Step3: Simplify left side

$5n + 161 -12 +30 +134 +16 +126 = 1080$
$5n + 455 = 1080$

Step4: Solve for $n$

$5n = 1080 - 455 = 625$
$n = \frac{625}{5} = 125$

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Step1: Find sum of interior angles (8 sides)

Sum = $(8-2)\times180 = 1080^\circ$

Step2: Set up angle sum equation

$130 + 129 + 116 + 120 + x + 125 + 135 + 120 = 1080$

Step3: Calculate known angle sum

$130+129+116+120+125+135+120 = 875$

Step4: Solve for $x$

$x = 1080 - 875 = 205$

Answer:

1. $x = 36$
2. $n = 125$
3. $x = 205$