 Question:

What is the number of sides of a regular polygon whose interior angles are \$3849_w34_h14.png\$ each? (Remember, the sum of exterior angles of any polygon is \$1912_w35_h12.png\$.)

A 15
Explaination

The sum of exterior angles of any polygon is always equal to 360 degrees, hence:
Exterior angle measurement in degrees x n = 360
where n is the number of angles (which is also the number of sides).
Also, for a given interior angle, the exterior angle = 180 – interior angle
In the problem: the exterior angle = 180 – 156 = 24 degrees
From the formula given above and measurement of the exterior angle computed: 24n = 360
\$8306_w144_h14.png\$
The polygon has 15 angles and 15 sides.
An alternative approach to this problem is to derive or remember that the measurement of each angle of a regular polygon can be determined using the formula: \$3981_w122_h39.png\$, where n is the number of sides and x is the measurement of the interior angle.
Substituting the given information, the equation becomes: \$9098_w139_h39.png\$, and solving for n gives 15.