Answer:
Step-by-step explanation:
Statements Reasons
1). Points A, B and C form the triangle 1). Given
2). Let DE be a line passing through 2). Definition of parallel lines
B and parallel to AC
3). ∠3 ≅ ∠5 and ∠1 ≅ ∠4 3). Theorem of Alternate
interior angles
4). m∠1 = m∠4 and m∠3 = m∠5 4). Definition of alternate angles
5). m∠4 + m∠2+ m∠5 = 180° 5). Angle addition and definition
of straight lines
6). m∠1 + m∠2+ m∠3 = 180° 6). Substitution
I)
Every 8.th voter gets a button:
so a sequence of the voters who receive a button is:
8, 16, 24, 32, .... that is 8*1, 8*2, 8*3, 8*4, .... in general: 8k for some integer k
ii)
Every 10.th voter gets a sticker, so the voters who receive stickers are the :
10, 20, 30, 40, .... voters that is 10*1, 10*2, 10*3, 10*4... in general 10t
for some integer t
iii) what we are looking for is the first number which is 8k and 10t at the same time.
8k=2*2*2k,
10t=2*5t
Thus this number must be divisible by 2*2*2*5*{some positive integer}
the smallest number is when the positive integer is 1, thus the number is
2*2*2*5=8*5=40
Answer: g. the 40th