Quadrilateral abcd is inscribed in circle 0. chords ba and cd are extended to intersect at point e. a tangent at b intersects line da where lineda is extended to point f. diagonals bd and ac of quadrilateral abcd are drawn.arch āb =128arch bc =144°arch dc = 64arch da = 32find the measure of angle 1,2,5 and 6

Check the picture below.

let's notice the "white" ∡1 is an inscribed angle with an intercepted arc of (x-32), and the "green" ∡5 is also an inscribed angle with an intercepted arc of (2x).

the ∡6 and ∡2 are both external angles, however they intercepted two arcs, a "far arc" and a "near arc", thus we'll use the far arc - near arc formula, as you see in the picture, and we'll use the inscribed angle theorem for the other two.