Question

Can someone please help me with this problem (Picture In comments)

Answer 1

what problem?

Answer 2

a. 45º

Answer 3

is it beacuse AC is 45?

Answer 4

yes, i guess that's arc of that angle

Answer 5

b. 45º

Answer 6

c.45º

Answer 7

d.90º

Answer 8

e.45º

Answer 9

f.90º

Answer 10

Thank you sooo muchh.

Answer 11

angle 4 = 62.5 as its half the arc BC and arc BC = 135

Answer 12

I would say angles 1 and 2 are 67.5 as well : sum of intercept arcs / 2

(angle 4 is 67.5 as well, forgot to carry a one there ;-) )

Answer 13

Thanks for the corrections. campbell_st & m_charron2

Answer 14

So it would be

A. 67.5
B. 45
C. 45
D. 62.5
E. 45
F. 90
??

Answer 15

D is 67.5 as well actually. since the arc is 90+45 = 135, your angle is going to be 135/2, which is 67.5

Answer 16

more importantly, do you get how we came up with these answers?

Answer 17

No, would you care to explain to me ?

Answer 18

sure, not a problem. Ok ,for question 1, it's pretty obsivous that angles 1 and 2 are the same, and since we know what the measure of the arcs are, we can use this formula :
angle 1 = angle 2 = (arc EB + arc AC) /2 = (90+45)/2.

For 2), angle 3, there are a few ways to get there, the easiest is a formula again. the intercepted arc for the segments BF and BD is arc BF. There are no arcs intercept by the other side of that angle, right? So, same formula, angle 3 = (arc BF + 0)/2, so we get 45 degrees

More to come

Answer 19

for 3), arc CF, you know that the arc AFB is 180 degrees since AB is a diameter. you know arc AC and arc BF so we can write this :
arc ABF = arc BF + arc FC + arc AC
180 = 90 + arc FC + 45
arc FC = 45

For 4), same thing as #2), we have 2 segments intercepting only one arc, arc BC, so using the formula
angle 4 = (arc BC + 0)/2 = (arc CF + arc FC + 0)/2 = (90+45+0)/2 = 135/2 = 67.5

Answer 20

5) is easy, you have the other 2 interior angle of the triangle (67.5 and 67.5) so you can just substract them from 180 and you're all set (or we can use the same formula again, but you'd need to find arc AE first)

And finally, 6) is that AE which I was talking about. 2 ways to get it, either you use the formula again, giving you this :
angle 5 = 45 = (arc AE + 0)/2
arc AE = 45 * 2 = 90
Or simply, you know that arc AEB is 180 degrees (because AB is a diameter) and you get this :
arc AEB = arc AE + arc EB
180 = arc AE + 90
arc AE = 90

And we're done

Answer 21

Ohhhhhhh okayyy, It was actually very easy once you explained it to me. At a first glance at the picture I thought it was hard. But once I understood it, it was fairly easy. Thank you soo much for all your explanations and help.

Answer 22

not a problem :-)