Question

9.
$x = \underline{\quad\quad}$
10.
$x = \underline{\quad\quad}$
11.
$x = \underline{\quad\quad}$
12.
$x = \underline{\quad\quad}$

Explanation:

Problem 9

Step1: Sum exterior angles of polygon

For any convex polygon, the sum of exterior angles is $360^\circ$.

Step2: Set up angle sum equation

$55^\circ + 60^\circ + 55^\circ + x^\circ + 55^\circ + 60^\circ = 360^\circ$

Step3: Calculate known angle sum

$55+60+55+55+60 = 285$

Step4: Solve for $x$

$x = 360 - 285 = 75$

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Problem 10

Step1: Sum exterior angles of polygon

For any convex polygon, the sum of exterior angles is $360^\circ$.

Step2: Set up angle sum equation

$20^\circ + 94^\circ + 20^\circ + x^\circ = 360^\circ$

Step3: Calculate known angle sum

$20+94+20 = 134$

Step4: Solve for $x$

$x = 360 - 134 = 226$

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Problem 11

Step1: Sum exterior angles of polygon

For any convex polygon, the sum of exterior angles is $360^\circ$.

Step2: Set up angle sum equation

$(2x-20)^\circ + 110^\circ + x^\circ + 120^\circ = 360^\circ$

Step3: Simplify the equation

$2x - 20 + 110 + x + 120 = 360$
$3x + 210 = 360$

Step4: Solve for $x$

$3x = 360 - 210 = 150$
$x = \frac{150}{3} = 50$

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Problem 12

Step1: Sum exterior angles of polygon

For any convex polygon, the sum of exterior angles is $360^\circ$.

Step2: Set up angle sum equation

$x^\circ + 60^\circ + x^\circ + 83^\circ + 63^\circ = 360^\circ$

Step3: Simplify the equation

$2x + 60 + 83 + 63 = 360$
$2x + 206 = 360$

Step4: Solve for $x$

$2x = 360 - 206 = 154$
$x = \frac{154}{2} = 77$

Answer:

1. $x = 75$
2. $x = 226$
3. $x = 50$
4. $x = 77$