Question

Find the measure of the following numbered angles in circle P when arc AE = 53°,
arc BA= 68°, and arc CB = 72°.
find angle measure 1.

Answer 1

I also have to find angle measures 2, 3, 4, 5, 6, 7, 8.

Answer 2

a straight line has angle measure 180° ... in your diagram arc BE is 180°
so if BE is 180° and AE is 53° what is AB?

Answer 3

oh, so AB has to be =127?

Answer 4

exactly

Answer 5

so would angle 1 and 3 be the same?

Answer 6

are those parallel lines intersecting the same line?

Answer 7

no...

Answer 8

but doesn't it have the little half circle that makes it congruent?

Answer 9

is anything else given besides those 3 angle measures?

Answer 10

no. I'm really confused, sorry.

Answer 11

I am too, don't see how to get any of the other angles
but since it is circle P, the lengths of PE = PB = PD

Answer 12

um, how can I use that information for the questions? I don't think I have any parallel lines to work with.

Answer 13

ok, what do the angles of a triangle add up to? look at the triangle with base BD and you can get angle 3

Answer 14

180 per triangle right?

Answer 15

yes

Answer 16

so, would it be 60?

Answer 17

and if DH is a tangent to circle P, then angle 4 is 90°

Answer 18

I don't think it is 60, but that's very very close

Answer 19

okay, um....

Answer 20

59?

Answer 21

that looks better

Answer 22

soo wouldn't angle 2 be the measure of half that of angle four?

Answer 23

why would that be?

Answer 24

wait, nevermind I looked at it wrong.

Answer 25

forget all I just told you... I set it up wrong...
arc AE does not tell you anything about the angles at point F
sorry
best bet is to delete all this or post it again

Answer 26

but the sum of the angles in a triange is 180
and opposite angles are the same
and angles on a straight line are 180

Answer 27

angle BPE is 121

Answer 28

um okay, are all of the answers wrong? like, should I not use them to find the other angles?

Answer 29

right, except PDH is 90... property of a tangent, if that is one

Answer 30

BPE is isoscolese triangle so you know those 3 angles (angle BPE is 53+68)

Answer 31

add line PC and you know that BPC = 72, so you can find CPD
and then triangle CPD is isoscolese so you can get those angles around D

Answer 32

well, that's about all I can do right now, hope it helped a little...
but it has been 30 years since my last geometry class...
EBC is 29.5°
PDH is 90° if that is a tangent
CDH is 54°