Inscribed angle geometry question (pic included)

Question

anonymous · Answer

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owlcoffee · Answer

There is always some confusion where to start in these kind of excercises, but the ONLY way to start is to start from the given information.
But I have to suppose you know some already, So I will help you start out.
Since AB is congruent to CB we will know that since they compose a triangle with the diameter of the given circle, we will say then that ABC is an iscoceles triangle.

An isoceles triangle has two pairs of equal angles, those are "<ACB" and "<CAB"

anonymous · Answer

so in that top angle, angles a and c would be 45 degrees

anonymous · Answer

i'm lost as to where to go from there

owlcoffee · Answer

A Hint: "When two chords join with the diameter, the middle angle will be a right angle".
in this case angle B and angle E are 90 degree