Question

If m angle BAC=55 degrees, what is m angle DBC? Picture included.

1) 20 degrees
2) 80 degrees
3) 70 degrees
4) 35 degrees

Answer 1

4) 35 degrees

Answer 2

If someone could help me figure it out on my own for future times would be nice.

Answer 3

chord BD goes through the center of the circle, so BD is a diameter

that means that arc DAB is 180 degrees and arc BCD is also 180 degrees

Answer 4

So how do I find what B is?

Answer 5

use the inscribed angle theorem to get

minor arc BC = 2*(angle BAC)

minor arc BC = 2*(55)

minor arc BC = 110 degrees


Now we use the fact that arc BCD is 180 degrees to find minor arc CD


(minor arc BC) + (minor arc CD) = arc BCD

(110) + (x) = 180

110 + x = 180

x = 180 - 110

x = 70

So minor arc CD is 70 degrees


After you find that minor arc CD is 70 degrees, you cut that in half to get 35 degrees (since the inscribed angle is half the central angle)

Answer 6

So this means that angle DBC is 35 degrees (because angle DBC is an inscribed angle that subtends minor arc CD)

Answer 7

Got it. Added to my notes. Thank you very much!

Answer 8

you're welcome