A regular polygon has interior angles of 150∘. A,B,C,D are 4 consecutive points of this polygon. What is the measure (in degrees) of ∠ADC?

150n = 180(n-2)

n = 12

So, the figure is a 12-gon
That should get you started

30 degrees

To find the measure of ∠ADC in a regular polygon with interior angles of 150∘, we need to find the number of sides in the polygon first.

The formula to find the measure of each interior angle of a regular polygon is:

Interior Angle = (n-2) * 180 / n, where n is the number of sides in the polygon.

Here we know that the interior angle is 150∘, so we can set up the equation as follows:

150 = (n-2) * 180 / n

Now, we can solve for n:

150n = 180(n-2)
150n = 180n - 360
30n = 360
n = 12

So, the regular polygon has 12 sides.

Now, we can find the measure of ∠ADC.

Since A, B, C, D are consecutive points on the polygon, they create one side of the polygon. And since the polygon has 12 sides, each angle formed by two consecutive points will be 360/12 = 30 degrees.

Therefore, the measure of ∠ADC is 30 degrees.