The sum of the interior angles of any polygon can be found by using the following formula:
180 (n -2), where n is the number of sides of the polygon.
In this case, we have a 4 sided kite. So, when we plug 4 into our formula, it is re written as such:
180 (4-2)
= 180 (2)
= 360
So the sum of the interior angles of the kite must equal 360°.
We know from polygon and quadrilateral rules that kites must have one set of congruent opposite angles. To find the sum of the remaining two angles in this kite, we can determine the difference between 360° and the sum of the non-congruent opposite angles (which is given in the problem).
The solution is as follows:
105 + 100 = 205
360 - 205 = 155
Thus, 155 is the sum of the remaining two opposite angles. We know one of these has to 100°, because the kite has to have one set of congruent opposite angles. This means the measure of angle DCB is 55°.
To check, we can add these two angles together and if we are correct we should get 155.
100 + 55 = 155.
