22.04.2023

# A partial proof was constructed given that MNOP is a parallelogram. Which statement should fill in the blank in the last line of the proof? A. angle M is supplementary to angle O. B. angle N is supplementary to angle P. C. angle M is congruent to angle P D. angle N is congruent to angle P. 30

17.02.2022, solved by verified expert

### Faq

Mathematics

last notation is right N =~ P

Step-by-step explanation: this is because any angle equals 180° but not less than 90° are regarded as supplementary angles. This means N<= 180°, P<= 180°

Mathematics
∠M ≅ ∠O; ∠N ≅ ∠P

Step-by-step explanation:

According to the problem   Which means, And, Therefore, the right answer is the last choice. Mathematics
From the above information we are told that MNOP is a parallelogram with <M supplementary to <N, <P supplementary to <M and  <N supplementary to <O. We can therefore deduce that <O is supplementary to <P if OP will act as the transversal to MP and NO also, <O-=<M
Mathematics
A diagram of parallelogram MNOP is attached below

We have side MN || side OP and side MP || NO

Using the rule of angles in parallel lines, ∠M and ∠P are supplementary as well as ∠M and ∠N.

Since ∠M+∠P = 180° and ∠M+∠N=180°, we can conclude that ∠P and ∠N are of equal size.

∠N and ∠O are supplementary by the rules of angles in parallel lines
∠O and ∠P are supplementary by the rules of angles in parallel lines

∠N+∠O=180° and ∠O+∠P=180°

∠N and ∠P are of equal size

we deduce further that ∠M and ∠O are of equal size

Hence, the correct statement to complete the proof is

∠M ≅ ∠O; ∠N ≅ ∠P Mathematics
Mathematics

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

Mathematics
Answer: 440 grams for 1.54 is the better value
Explanation:
Take the price and divide by the number of grams
1.54 / 440 =0.0035 per gram
1.26 / 340 =0.003705882 per gram
0.0035 per gram < 0.003705882 per gram
Mathematics

Cost of 7 gallons=$24.50 Cost of 1 gallon=24.50/7=3.5 Cost of 15 gallons=15*3.5=52.5 Cost of 15 gallons will be$52.5

Mathematics

For 1 flavor there are 9 topping

Therefore, for 5 different flavors there will be 5*9 choices

No of choices= 5*9

=45

Mathematics  