Answer:
x°=38°
y°=22°
Explanation:
The angle that lies between a tangent and a chord is equal to the angle subtended by the same chord in the alternate segment (see image below of example of this if this explanation's unclear). This means:
<UDC=<DAC
38°=x°
The circle contains a cyclic quadrilateral ABCD (a shape with four sides within a circle whose corners are all on the circle edge). Opposite angles in a cyclic quadrilateral total 180°, which means:
<ADC+<ABC=180°
60+<ABC=180°
<ABC=120°
Since DA is parallel to CB, <DAC and <ACB are alternate interior angles and therefore equal, which means <ACB=<DAC=x°=38°
The angles in a triangle always add to 180°. Considering triangle ABC, this means:
<CAB+<ABC+<ACB=180°
y°+120°+38°=180°
y°=180°-158°=22°