Question

Find the measure of angle BAC

Answer 1

Any numbers?

Answer 2

The number in the center is 68
@Directrix

Answer 3

and the possible answers are
A. 57 degrees
B. 114 degrees
C. 66 degrees
D. 123 degrees

Answer 4

Do you know how many degrees are in a circle?

Answer 5

360

Answer 6

correct. now you see that the line AC is bisecting that circle in half right? How many degrees does that leave you if you cut the circle in half?

Answer 7

Here is the marked up diagram. I will wait until heycoa finishes working with you.
@blossombuttercupandbubbles1234

Answer 8

@Directrix I think I am finished working with heycoa. I saw your diagram and i was wrong the numbder in the middle is 66

Answer 9

whoops, I could not make out the first picture, I was not doing the problem correctly!

Answer 10

Maybe this is the correct diagram.

Answer 11

Yep that works! 66 + 114 = 180

Answer 12

@Directrix

Answer 13

How do you get the measure of an inscribed angle of a circle? What does that theorem state? @blossombuttercupandbubbles1234 @heycoa

Answer 14

the measure of an inscribed angle is half the measure of its intercepted arc

Answer 15

@Directrix

Answer 16

Yes, and the measure of the intercepted arc is what? @blossombuttercupandbubbles1234

Answer 17

Look at the diagram.

Answer 18

@Directrix 66?

Answer 19

Look on the diagram to see where I extended the "jaws" of the angle at B and C. The angle "bites off" the blue arc. It has measure 114. So, take half of 114 and you get ? @blossombuttercupandbubbles1234

Answer 20

@Directrix I get 57. I would add 57 + 66 and get the measure of angle BAC. Is this right?

Answer 21

114 divided by 2 = 57. I get 57 for the measure of the angle BAC. Look at the diagram and see if I marked the letters in the right place. It was hard to see on the original diagram you posted.

Answer 22

@Directrix yeah I know it was really fuzzy, but look on the bright side you will get best answer.
My next question is this:
Given that angle DAB and angle DCB are right angles and m ACD = 310, what is the measure of angle ADB
A. 51 degrees
B. 65 degrees
C. 33 degrees
D. 115 degrees

Answer 23

See if you agree with the diagram.
Is the measure of arc AB = 130?

Answer 24

@Directrix Yes if AD is 50

Answer 25

Then AB is 130

Answer 26

What is the measure of ADB though,

Answer 27

Arc DAB is a semicircle. That right angle is inscribed so it cuts off a 180 degree arc. Segment BD is the diameter of the circle.

Answer 28

Angle ADB is an inscribed angle. How do you get the measure of an inscribed angle of a circle. We just did that on the previous problem.

Answer 29

Yes, half of 130 = 65
or is it half of 65
@Directrix

Answer 30

Half of the arc it bites off. So --> Yes, half of 130 = 65

Answer 31

So then is the measure of the angle ADB 65?

Answer 32

@Directrix do you think that's right?

Answer 33

Yes, I do. @blossombuttercupandbubbles1234

Answer 34

@Directrix Great Thanks! I have one more question and that will be my last for the night!
If m BY= 38, what is m YAC?
A. 128 degreed
B. 109 degrees
C. 71 degrees
D. 218 degrees

Answer 35

You draw the diagram and mark it up this time around.

Answer 36

@Directrix