I have a few questions in math, i was wondering if someone could help me?

Question

ANSWER CHOICES:
A. 61
B. 100
C. 21
D. 42
E. 14.8
F. 33
G. 36
H. 80
I. 12
J. definition of congruent angles
K. 35
L. 1/2
M. 40
N. 6
O. 16.5
P. 13.5
Q. 50
R. 1
S. 70
T. 55
U. 45
V. substitution
W. 4
X. 110
Y. 9
Z. 18

Figure 4: GH and JK are chords of the circle.
Figure 5: PE and PF are tangent segments.

Below is the site to the diagrams, figure 4 and 5:
http://www.learningbygrace.org/geom/images/geom_26.2.4,5.jpg

Question 1:
In Figure 4, if m Arc GJ = 40 and m Arc HK = 82, m Ang KIH =

Question 2:
In Figure 4, if m Ang KIH = 60 and m Arc HK = 80,, m Arc GJ =

Question 3:
In figure 5, if m Arc EF = 100, then m Ang P =

Question 4:
In figure 5, if m Arc EXF = 250, then m Ang P =

Question 5:
In Figure 4, if GI = 7, JI = 14, and IK = 9 what is IH?

Question 6:
In Figure 4, if GI = 3, IH = 8, JK = 10, what is JI (if it is longer than IK)?

Question 7:
In Figure 4, if GH = 8, JI = 8, IK = 2, what is GI?

Question 8:
In Figure 4, if GI = 8, IH = 6, JI = 10, what is JK?

Answer 1

Hi,



Question 1:

In Figure 4, if m Arc GJ = 40 and m Arc HK = 82, m Ang KIH =



The angle formed when 2 chords intersect is the average of the arcs.

40 + 82

----------- 61 = m
......2



Question 2:

In Figure 4, if m Ang KIH = 60 and m Arc HK = 80,, m Arc GJ =



HK + GJ

------------- = m
.......2



80 + GJ

------------- = 60

.......2



80 + GJ = 120

GJ = 40



Question 3:

In figure 5, if m Arc EF = 100, then m Ang P =



The measure of an exterior angle formed by 2 tangents is:



BIG arc - small arc

-------------------------- = m exterior angle

...............2



If EF = 100, then arc EXF = 260.



260 - 100

-------------- = 80

........2





Question 4:

In figure 5, if m Arc EXF = 250, then m Ang P =



BIG arc - small arc

-------------------------- = m exterior angle

...............2



250 - 110

--------------- = m exterior angle

.........2



140/2 = 70 = m exterior angle





Question 5:

In Figure 4, if GI = 7, JI = 14, and IK = 9 what is IH?



The product of 2 parts of one chord equal the product of the 2 parts of the other chord. For this problem, GI*IH = JI * IK.



GI*IH = JI * IK

7*IH = 14 * 9

7*IH = 126

IH = 18





Question 6:

In Figure 4, if GI = 3, IH = 8, JK = 10, what is JI (if it is longer than IK)?



GI*IH = JI * IK

3*8 = JI * IK

24 = JI * IK

If JK is 10, then JI = x and IK = 10 - x

24 = x(10 - x)

24 = 10x - x²

x² - 10x + 24 = 0

(x - 6)(x - 4)

The 2 pieces are 4 and 6, but JI is longer so it equals 6.





Question 7:

In Figure 4, if GH = 8, JI = 8, IK = 2, what is GI?



GI*IH = JI * IK

x*(8 - x) = 8 * 2



x² -8x + 16 = 0

(x - 4)² = 0

x = 4

GI = 4





Question 8:

In Figure 4, if GI = 8, IH = 6, JI = 10, what is JK?

GI*IH = JI * IK

8*6 = 10*IK

48 = 10IK

4.8 = IK

JK = 14.8





Summary of answers.



1A 61

2M 40

3H 80

4S 70

5Z 18

6N 6

7W 4

8E 14.8



I hope that helps!! :-)

Answer 2

1. R

2. C

3. K

4. A

5. Q

6. E

7. G

8. J

Answer 3

1. f

2. e

3. t

4. w

5. h

6. n

7. c

8. a