Answer:
x = 93°
y = 97°
Step-by-step explanation:
Angle y
A cyclic quadrilateral is a quadrilateral drawn inside a circle where every vertex touches the circumference of the circle.
The opposite angles in a cyclic quadrilateral add up to 180°
⇒ y = 180° - 83°
⇒ y = 97°
Angle x
Inscribed Angle Theorem: the measure of an inscribed angle is half the measure of its intercepted arc.
Inscribed angle: an angle with its vertex on the circle and whose sides are chords.
Intercepted arc: the arc that is inside the inscribed angle and whose endpoints are on the angle.
x is an inscribed angle and (122° + 64°) is its intercepted arc.
⇒ x = (122° + 64°) ÷ 2
⇒ x = 93°
