The value of y is 50
The angle measurement of angle AOB is 100°
Circle Geometry
From the question, we are to determine the value of y and the measure of angle AOB
From one the circle theorems, we have that
Angles in the same segment are equal
In the given diagram, x° and y° are angles in the same segment
∴ x° = y°
From the given information,
x = 50
∴ y = 50
Hence, the value of y is 50
Also, from another circle theorem,
Angle at the center is twice the angle at the circumference
∴ ∠AOB = 2x° = 2y°
Then,
∠AOB = 2×50°
∠AOB = 100°
Hence, the angle measurement of angle AOB is 100°
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