A. angle CXD = 140 degrees
Angle XCD and Angle XDC are congruent since the triangle is isosceles. Remember that the sum of the interior angles of a triangle is 180 degrees.
20 + 20 + x = 180
x = 140
B. 18 sides
To find the number of sides of the polygon, we need to know the measure of one interior angle. One interior angle is angle BCD. We can easily find the measure of this angle because it is on a straight angle of which we are given part of (angle XCD).
Angle XCD + Angle BCD = 180
20 + BCD = 180
BCD = 160
Now that we know the measure of an interior angle, we can use the formula to find the measure of an interior angle and algebraically solve for the number of sides.
[ (n - 2) x 180 ] / n = 160
(n - 2) x 180 = 160n
180n - 360 = 160n
-360 = -20n
n = 18 sides
C. 2880 degrees
The formula for the sum of the interior angles of a regular polygon is (n - 2) x 180, where n is the number of sides.
(18 - 2) x 180
16 x 180
2880
D. 140 degrees
If angle XCD is 20 degrees, then angle BED is also 20 degrees. Angle BED and Angle BEF make up one of the interior angles of the regular polygon. We know that one interior angle is equal to 160 degrees.
Angle BED + Angle BEF = 160
20 + BEF = 160
BEF = 140
Hope this helps!