This figure shows circle o with inscribed ∠xyz. m∠xyz=76∘ what is the measure of xyz?

Check the picture below.

now, the inscribed angle is at ∡XYZ and is 76°, that means by the "inscribed angle theorem", the intercepted arcXZ, in red, is twice as much, namely 152°.

keeping in mind that a circle has a total of 360°, and since the red arc has already taken up 152°, the arcXYZ in blue, will pick up the slack from 360° - 152°, namely 208°.