Question

easy/medium geometry question. I've gotten really rusty at this.

so far, I've found
angle 4= 90
angle 8 = 90

maybe angle 1 = 63.5
angle 4 maybe = 116.5

These are the answer choices to match with.
29.5°
121°
124 °
54°
116.5°
63.5°
90°

Answer 1

https://banff.owschools.com/media/g_geo_2013/7/group156.gif

Answer 2

** angle 6= 116.5

is there a way to explain how we get these answers? : o aside from using compass, etc.

Answer 3

are we given that BD = diameter and DH = tangent ?

Answer 4

I think it is tangent.

Answer 5

whats the given info ?

Answer 6

but I'm not positive that angle 4 is 90.

Match angles 1-7 with the following degrees

Answer 7

angle 4 is 90 if DH is tangent cuz \(\large \text{radius} \perp \text{tangent}\)

Answer 8

ok that's true, then angle 4 is 90. How do I continue?

Answer 9

you're correct about angle 8 too, it has to be 90 as it is a semicircle angle

Answer 10

Oh that's lucky : D , what about 1 and 6? Since they add up to be a straight line, I just try to find 2 answer choices that sums to 180... not sure if it's right though.

The rest, I'm stuck.

Answer 11

angle6 = 116.5°
angle1 = 63.5°

(why ?)

Answer 12

we're on same page on that :)

Answer 13

only those two angles addup to 180 in the given options, so we can conclude on angles 1 and 6

Answer 14

now we have to find other angles with what we know so far.
I searched up a list of circle properties, not sure if we can apply anything here.

Answer 15

http://connectatkmtc.files.wordpress.com/2012/04/cnc_aag.jpg

Answer 16

angle 1 = angle 3 + (angle 2 - angle 4)

Answer 17

therefore angle 3 + angle 2 = 153.5

Answer 18

that gives relation between angles 2 and 3
lets try and get another relation between them so that we can solve the system of equations

Answer 19

great! Now it looks a little bit more solvable :))

Answer 20

lets look at angle 5 :

Answer 21

those two angles will be same

Answer 22

ohh I see that now : o

Answer 23

for some reason I thought angle 5 = 45, but that's not true right?

Answer 24

one more relation :

angle 3 = (180 - angle 7)/2

Answer 25

ohhh because it's the triangle is made up of two radius and a line , isosceles triangle

Answer 26

inscribed angle = (central angle) / 2

Answer 27

I see : o I forgot that formula.