In the figure angle x and y are
1. x = 90 degrees and y = 65 degrees
2. x = 160 degrees and y = 80 degrees
3. z = 160 degrees
x = 175 degrees
y = 130 degrees
How to find the values of x and y
1. angle x = 90 degrees (angle on a semicircle)
assuming angle C is 25 degrees
25 + y = 90 degrees (complementary angle)
y = 90 - 25
y = 65 degrees
2. y = 80 degrees (angles are intercepting equal arc)
x = 80 * 2 (intercepted arc measure = inscribed angle * 2)
x = 160 degrees
3. z = 80 * 2 (intercepted arc measure = inscribed angle * 2)
z = 160 degrees
x = HKJ / 2 (intercepted arc measure = inscribed angle * 2)
HKJ = 360 - 50 - z (sum of angles of a circle)
HKJ = 360 - 50 - 160
HKJ = 150
therefore, x = 150 / 2 = 75 degrees
y = 360 - 80 - 75 - x (sum of angles of a quadrilateral)
y = 360 - 80 - 75 - 75
y = 360 - 230
y = 130 degrees