TITLE: what is the angle here in this cyclic triangle?
QUESTION [7 upvotes]: If I join the chord then I am getting the angles of the triangle are $45,45,90$ so $\theta=180-2x$ where $x$ is the angle of the other triangle whose angle is $\theta$

REPLY [3 votes]: Draw the rest of circle (complete the circle), 
Inscribed Angle =(1/2)Intercepted Arc


$$m(\widehat{CDB})=\frac{1}{2}m( \stackrel \frown{CEB})$$
$$m(\widehat{CDB})=\frac{1}{2}270^{o}=135^{o}$$