NEED HELP WITH GEOMETRY!

[chuckjefster90]

Hey Guys,
Please help me with geometry! ive attached a excercise im suppose to do but have no clue about!
Questions 1a,c,e   2a,b,e     3a,c,e      4a,c,e

Could you please explain to me how to work these out!
Im struggling so much!

Will really appreciate it HEAPS!

THANK YOU!

[|ll|lll|]

1a) 60 (angles at circumference)
c) 27 (angle at centre = twice angle at circum.)
e) f = 36 (same reason as in c); g = 54 (angles in an isos. triangle)

2a) w = 3 (angles at circumference)
b) v = 104/13 (angle at centre = twice angle at circum.)

Lol I'll get others to help you with the rest. You should be able to get a gist of circles now

[brightsky]

2e) Draw the angle at the circumference that subtends the same arc as angle e in the centre. Then you'll be making a cyclic quadrilateral so the angle you have drawn at the circumference would be 180 - 116 = 64. Then use the law that angles at the centre are twice that of the circumference so e = 2*64 = 128.

3a) a = 25 (angles at the centre are twice angles at the circumference)
c) a = 35 (angles at the circumference subtending the same arc are equal)
    b = 45 (same reason as above)
    c = 100 (triangles at up to 180 + vertically opposite angles are the same)
e) x = 56 (angles at the centre are twice angles at the circumference)
    y = 62 (isosceles triangle, base angles are equal - isosceles triangle because radii are equal)

4a) a = 90 (angle at the centre are twice angles at the circumference)
c) b = 180 - 90 - 50 = 40 (using same logic as above)
e) e = 180 - 50 - 50 = 80 (using logic above and that base angles are equal in isosceles triangle - radii are equal in this case again)