What is the answer to my question as how did you get it.

  305°

Step-by-step explanation:

Central angles APC and DPE are "vertical angles" so both have the marked measure 93°. Central angle APB is 38° less than this, so is 55°. This is also the measure of short arc AB. The measure of arc AEB is the rest of the circle, so is the difference between arc AB and 360°, so is ...

  arc AEB = 360° -55°

  arc AEB = 305°

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.