Question

Is my answer correct? Someone check please :D


I got either 40 for the question attached below. Am I correct? Another answer I got was 190 when I switched them around.

Answer 1

x=1/2(140+90)

Answer 2

x=185

Answer 3

i dont remember the name of the theorem that sates that

Answer 4

@opern1112

Answer 5

I don't know the name either, but it's theorem 4 on this page

http://www.regentsprep.org/regents/math/geometry/gp15/circleangles.htm

Answer 6

I solved it like 140=1/2(x+90) and 90=1/2(x+140)....

Answer 7

it's actually

\[\Large x = \frac{1}{2}(140+90)\]

as AlexandervonHumboldt2 stated and as the link states

Answer 8

How did Alexander get x=185?? I got x=115 if solved in the way mentioned.

Answer 9

maybe i mistaked

Answer 10

yeah 115

Answer 11

What if AD was 78 and BC was 116? It says the correct answer is 154 degrees for this question.

Answer 12

Then you'll have

\[\Large x = \frac{1}{2}(78+116)\]

Answer 13

and yeah,

\[\Large x = \frac{1}{2}(140^{\circ}+90^{\circ}) = 115^{\circ}\]

Answer 14

But the correct answer is 154... The x is on the outside of the circle near BC, unlike the first question where x is inside the circle near the center of arc BC

Answer 15

Wouldn't 1/2(78+116) give 97? The correct answer is 154.
The response feedback was that they solved it by 116=1/2(x+78)

Answer 16

oh they moved that x to a different spot

Answer 17

I thought x stayed at the intersection of the two secants

Answer 18

Is there a difference with x staying in the inside and outside of the circle??

Answer 19

so yeah, it's

\[\Large 116 = \frac{1}{2}(x+78)\]

assuming the arc measures are x and 78

Answer 20

the stuff inside the parenthesis are the arc measures