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5. b) Find the number of sides of the polygon.

Determine the measure of the exterior angle.
From part a), we found $x = 30$ . The exterior angle is $x^\circ$ , so the exterior angle is $30^\circ$ .
Calculate the number of sides of the polygon.
For any regular polygon, the sum of its exterior angles is $360^\circ$ . The number of sides ( $n$ ) is found by dividing $360^\circ$ by the measure of one exterior angle.
$n = \frac{360^\circ}{\text{Exterior Angle}}$ $n = \frac{360^\circ}{30^\circ} = 12$
The number of sides of the polygon is $\boxed{12}$ .

6. a) Simplify: $\frac{1}{2} + \frac{1}{3} \times \frac{1}{4}$
Perform the multiplication first, according to the order of operations (BODMAS/PEMDAS).
$\frac{1}{3} \times \frac{1}{4} = \frac{1 \times 1}{3 \times 4} = \frac{1}{12}$
Add the result to $\frac{1}{2}$ .
Find a common denominator, which is 12.
$\frac{1}{2} + \frac{1}{12} = \frac{6}{12} + \frac{1}{12}$ $\frac{6+1}{12} = \frac{7}{12}$
The simplified expression is $\boxed{\frac{7}{12}}$ .

6. b) Evaluate: $\frac{0.3 \times 0.4 - 0.06}{0.02}$
Perform the multiplication in the numerator.
$0.3 \times 0.4 = 0.12$
Perform the subtraction in the numerator.
$0.12 - 0.06 = 0.06$
Perform the division.
$\frac{0.06}{0.02}$
To simplify, multiply the numerator and denominator by 100 to remove the decimals.
$\frac{0.06 \times 100}{0.02 \times 100} = \frac{6}{2} = 3$
The evaluated expression is $\boxed{3}$ .

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