70580/02/SP/25©Cambridge U niversity Press & Assessment 2022 [Turn over13 Find the number of sides of a regular polygon with interior angle 162°.

To find the number of sides of a regular polygon, you can use the formula for the measure of each interior angle:

Interior Angle = (n-2) * 180 / n

where n is the number of sides.

In this case, you know the interior angle is 162°. So you can set up the equation:

162 = (n-2) * 180 / n

To solve for n, you can first multiply both sides by n to get rid of the fraction:

162n = (n-2) * 180

Then distribute the 180 to both terms on the right side:

162n = 180n - 360

Next, subtract 180n from both sides to get all the n terms on one side:

-18n = -360

Finally, divide both sides by -18 to solve for n:

n = 20

So, the regular polygon has 20 sides.