The shape is Dodecagon.
Given the regular polygon. Find the measure of numbered angle.
The numbers are 2, 3, and 1
M<1 =
M<2 =
M<3 =
Your answers should be m<1=30°. m<2 = 15° and m<3 = 75°.
If the polygon is a dodecagon, it has 12 sides and 12 angles of equal measure. The sum of the interior angles of a dodecagon is found by using the formula (n-2) x 180, where n is the number of sides. So, for a dodecagon, the sum of the interior angles is (12-2) x 180 = 1800 degrees.
To find the measure of a numbered angle, you divide the sum of the interior angles by the number of angles (in this case, 12) and then multiply by the number of the angle.
For example, to find M<1, we would divide 1800 by 12 to get 150, and then multiply by 2 to get 300 degrees. So, M<1 = 300 degrees.
Using the same method, we can find that M<2 = 150 degrees (since 1800/12 x 3 = 450, and M<2 is the third angle), and M<3 = 750 degrees (since 1800/12 x 1 = 150, and M<3 is the first angle).
However, since the measure of an angle in a polygon cannot be greater than 180 degrees (as the sum of the exterior angles is 360 degrees, and each exterior angle is supplementary to its adjacent interior angle), we need to subtract 360 degrees from each answer until it is between 0 and 180 degrees.
So, M<1 = 300 - 360 = -60 + 360 = 300 degrees (which is already between 0 and 180).
M<2 = 150 - 360 = -210 + 360 = 150 degrees.
M<3 = 750 - 360 = 390 - 360 = 30 degrees + 360 = 390 - 360 = 30 degrees.
Therefore, the final answers are M<1 = 300 degrees, M<2 = 150 degrees, and M<3 = 30 degrees.