Sorry I'm not CPhill... but here.
Since we know supplementary angles and vertical angles, we can solve this easily.
Angle BCD=20 degrees
Angle CDA=115 degrees.
That means Angle CBA is also 115 degrees, which makes this shape a kite.
Hope this helped!
Here's away to prove this
Since AB =AD.....then in triangle DAB angles ADB and ABD are equal = [180 - 110]/2 =
70/2 = 35°
So angle CDB =180 -65 - 35 = 80°
And angle BCD = 20°
So...in triangle CDB angle CBD = 180 - 80 - 20 = 180 - 100 = 80°
But....in triangle CDB,angles CBD are equal
So....this means that CB = CD
But since CB = CD and AB = AD....then ABCD is a kite because it has two pairs of equal adjacent sides