Geometry Help.. Im Clueless?

Question

Okay i have no idea how to do this someone please help me figure this out or tell me how to do it. Cause my grades in geometry aint lookin that good. Im failing :(
*Answer Choices*
A. 61
B. 100
C. 23
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. 5.20
O. 16.5
P. 13.5
Q. 50
R. 70
S. 6
T. 55
U. 45
V. substitution
W. 4
X. 110
Y. 9
Z. 18

*Questions*
1:In Figure 1, if m Arc AB = 80 then m Ang C = ______°
2: In Figure 1, if m Ang C = 42, then m Ang D =______°
3: In Figure 1, if m Arc CD = 90, then m Ang A =______°
4: In figure 2, m Arc ST =______°
5: In Figure 2, m Ang YRS =______°
6: In Figure 2, Ang WRS =______°
7: In Figure 3, if m Arc PM = 40 and m Arc JKM = 210, then m Arc JP =______°
8: In Figure 3 if m Arc PM = 40 and m Arc JKM = 210, then m Ang PJK =______°
9: In Figure 3, if m Ang PJK = 37 and m Arc PM = 41, then m Arc MK =______°
10: In Figure 3, if m Ang PJK = 37 and m Arc PM = 41, then m Ang MJK =______°
11: In Figure 4, if m Arc GJ = 40 and m Arc HK = 82, m Ang KIH =______°
12: In Figure 4, if m Ang KIH = 60 and m Arc HK = 80,, m Arc GJ =______°
13: In figure 5, if m Arc EF = 100, then m Ang P =______°
14: In figure 5, if m Arc EXF = 250, then m Ang P =______°
15: In Figure 4, if GI = 7, JI = 14, and IK = 9 what is IH?
16:In Figure 4, if GI = 1.3, IH = 19.2, IK = 4.8, what is JI (if it is longer than IK)?
17: In Figure 4, if GH = 8, JI = 8, IK = 2, what is GI?
18: In Figure 4, if GI = 8, IH = 6, JI = 10, what is JK?
19:In Figure 6, if AT = 9, AR = 6, what is AS?
20: In Figure 6, if AR = 3, AS = 9, what is AT?

**Figure 1&2**
http://i96.photobucket.com/albums/l161/southern_gurl714/geom_26_2_12.jpg
**Figure 4&5**
http://i96.photobucket.com/albums/l161/southern_gurl714/geom_26_2_45.jpg
**Figure 3&6**
http://i303.photobucket.com/albums/nn154/3softball6/geom_26_2_36.jpg

Answer 1

By now you have solutions with explanations for qus 1 to 7.



8. m ang PJK = (1/2) arc PK (angle at the circumference is half the angle at the centre subtended by the same arc PK)

Now m arc KM = 210 - 180

..................... = 30°

therefore m arc PK = PM + MK = 70

Therefore m ang PJK = 70/2 = 35°



9. Using the same ideas, m arc PK = 2*37 = 74°

Therefore m arc MK = 74 - 41 = 33°



10. m ang MJK = 2*33 = 66°



11. m ang GKJ = 40/2 = 20°

m ang HGK = 82/2 = 41°

In the triangle KGI, exterior angle KIH = sum of interior opposite angles IKG and IGK

= 20 + 41 = 61°



12. m ang HGK = (1/2)* m arc HK = 40°

Therefore in triangle KGI,

exterior angle KIH = sum of interior opposite angles KGI, GKI.

.............. i.e. 60 = 40 + ang GKI

m ang GKI = 20

Therefore m arc GJ = 40



13. Since PE, PF are tangents, they touch the circle at rightangles to the radius drawn to the point of contact. So, if we call the centre of the circle O, the quadrilateral OEPF has two rightangles, therefore the remaining angles total 180°. Since angle EOF = 100°, therefore angle EPF = 80°



14. m arc EXF = 250

Therefore m arc EF = 360 - 250 = 110 (i.e. the minor arc EF)

Then by the same process as in q. 13 (sum of angles of quadrilateral OEPF),

m ang P = 180 - 110 = 70°



15. When two chords of a circle intersect, the products of their pieces are equal. Once again, that's not the sort of formal statement of the theorem that you'll find in a text book, but it means that in figure 4

GI*IH = JI*IK

7*IH = 14*9

IH = 18



16. 1.3*19.2 = JI*4.8

Hence JI = (1.3*19.2)/4.8 = 5.2



17. GI*IH = 8*2 = 16

and GI + IH = 8

The two numbers which multiply to give 16 and add up to 8 are 4 and 4.

Therefore GI = 4.



18. 8*6 = 10*IK

therefore IK = 4.8

Hence JK = 10 + 4.8 = 14.8



19. When from a point external to a circle you draw a tangent to a circle and draw a secant from the same point, the square of the length of the tangent is equal to the product of the pieces of the secant. That's not how the formal statement of the theorem goes, but it means that in figure 6,

AT^2 = AR*AS [ I guess we should really write m(AT) etc.]

Thus 9^2 = 6*AS

AS = 13.5



20. as above, AT^2 = 3*9

Hence AT = sqrt(27) = 3*sqrt(3) = 5.196 approx.

That's 5.20 correct to two decimal places.



Amazing what one can do on holidays sometimes!!

Answer 2

answer: First reorganize the variable and constants so all variables are to the left and constants to the right 2x - y = -4 Equation a million x - y = 2 Equation 2 upload Equation a million and 2 so as that y is bumped off 2x - x - y + y = -4 - 2 x = -6 Already all of us be attentive to the respond is (-6,-8) because of the fact x is -6 replace the fee of x it particularly is -6 into Equation 2 -6 - y = 2 y = -8 to that end the Ans is (-6, -8) To coach it replace (-6, -8) decrease back into Equations a million and 2 2x - y = -4 Equation a million 2x - y = 2(-6) - (-8) = -4 x - y = 2 Equation 2 x - y = -6 - -8 = -6 + 8 = 2

Answer 3

1/

40



2/

42



3/

45



4/

100



5/

50



6/

80