Question

If mR = 28°, find mO. The figure is not drawn to scale.
152°
28°
62°
56°

Answer 1

what do i do?

Answer 2

hmm im not sure at the moment

Answer 3

Hint:

Use the inscribed angle theorem

Answer 4

That's a pic of a central angle

Answer 5

here is an inscribed angle (that subtends, or cuts, the same arc)

Answer 6

all inscribed angles that cut the same arc as the central angle will be half as large as the central angle, so if we label the angles the following



then y = (1/2)x or x = 2y

according to the inscribed angle theorem

Answer 7

I'm still confused :(

Answer 8

say we know that the central angle is 90 degrees, this would make the inscribed angle to be (1/2)*90 = 45 degrees

Answer 9

so "O" in my pic is the inscribed angle?

Answer 10

no, O is the center of the circle

Answer 11

mO

Answer 12

angle NOQ is the central angle

angle NRQ is the inscribed angle

Answer 13

angle O is the central angle

Answer 14

because it's in the center of the circle

Answer 15

inscribed angle = (1/2)*[ central angle ]

Answer 16

what is the inscribed angle

Answer 17

what is the measure of NRQ

Answer 18

at the risk of sounding stupid i am not sure at this point

Answer 19

angle R = angle NRQ

Answer 20

so 28

Answer 21

inscribed angle = (1/2)*[ central angle ]

28 = (1/2)*[ central angle ]

find the "central angle"

Answer 22

56

Answer 23

you got it

Answer 24

Thank you !sorry it took so long...