Question

13) Circle O is shown with point A, B, C, and D on Circle O.


If x = 50, what is the value of y and the angle measurement of angle AOB?


y = _____

m
(25) (50) (100) (not enough information)

Answer 1

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°

Learn more on Circle Geometry here: https://brainly.com/question/17074363

#SPJ1