Question

In the diagram, point O is the center of the circle and mADB = 43°. If mAOB = mBOC, what is mBDC?


A) 45°
B) 43°
C) 41°
D) 37°
E) 33°

Answer 1

I can help!

Answer 2

thank you soo much!! that would be very much appreciated!(:

Answer 3

In order to find out what you need, you have to be able to find the measure of arc BC. Do you know how to do that? You have to go about it kind of indirectly. I can help you. You're in Geometry?

Answer 4

I do not know how to do that , yes this is geometry. I am taking it online in summer school because I never took this class!

Answer 5

Do you know how to find the measure of the arc that is intercepted by an inscribed angle? It's a formula of sorts.

Answer 6

i don't! /: im sorry, i feel so stupid!

Answer 7

Ok, the length of an arc that is intercepted by an inscribed angle is twice the measure of the angle. So if angle ADB is 43, what is the measure of arc AB? Arc AB is 43 * 2. Arc AB is 86.

Answer 8

ok, that makes sence now!

Answer 9

Um...don't feel stupid, please. I teach math every day to kids who say that and they always get it. You're not stupid, you just don't know how to do this yet. Stupid would be if you didn't care to learn it when you know you can.

Answer 10

Moving on...We know that arc AB is 86. We also see that angle AOB is a central angle and it also encloses arc AB. If arc AB is 86, what is the measure of angle AOB? Do you know?

Answer 11

would it be 43 since that is half of 86?

Answer 12

The rule for central angles is that they are equal to the arcs they enclose. It arc AB is 86, what is the measure of angle AOB (it is a central angle)?

Answer 13

so it would be 86, right?

Answer 14

Yes it would! Now we are also told that angle BOC is congruent or equal to angle AOB. So if they are equal, what is the measure of angle BOC?

Answer 15

86!(:

Answer 16

Ok, now that know the measure of angle BOC, we have to find the measure of angle BDC. Do you remember what the rule for inscribed angles is when you know the arc? We used it in reverse when we were told that ABD was 43 and we had to find the arc length of AB. The arc is twice the measure of the angle. So if the arc length of BC is 86, what is the measure of the angle enclosing it?

Answer 17

half of it?

Answer 18

Why, yes! It would be half of 86. What is half of 86?

Answer 19

43!!!(:

Answer 20

Is 43 one of your choices for an answer?

Answer 21

yes, its B!

Answer 22

Yay!!!!! You did it! See?! Now don't you feel smart?

Answer 23

ohh yes!!! thank you so soo much!!!(:

Answer 24

You're very welcome. Anything else, just ask! We love to help!

Answer 25

ok(: