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Mathematics : asked on chelsea73
 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.

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17.02.2022, solved by verified expert
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Nitin Arora
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Mathematics, English, Physics. Research Scholar at Indian Institute of Technology, Roorkee
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B

Step-by-step explanation:

B. angle N is supplementary to angle P

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Mathematics
Apartial proof was constructed given that mnop is a parallelogram. parallelogram m n o p is shown. by the definition of a parallelogram, mn ∥ po and mp ∥ no. using mp as a transversal, ∠m and ∠p are same-side interior angles, so they are supplementary. using no as a transversal, ∠n and ∠o are same-side interior angles, so they are supplementary. using op as a transversal, ∠o and ∠p are same-side interior angles, so they are supplementary. therefore, because they are supplements of the same angle. which statement should fill in the blank in the
Step-by-step answer
P Answered by PhD

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
Apartial proof was constructed given that mnop is a parallelogram. by the definition of a parallelogram, mn ∥ po and mp ∥ no. using mp as a transversal, ∠m and ∠p are same-side interior angles, so they are supplementary. using no as a transversal, ∠n and ∠o are same-side interior angles, so they are supplementary. using op as a transversal, ∠o and ∠p are same-side interior angles, so they are supplementary. therefore, and because they are supplements of the same angle. which statements should fill in the blanks in the last line of the proof? ∠m
Step-by-step answer
P Answered by PhD
∠M ≅ ∠O; ∠N ≅ ∠P

Step-by-step explanation:

According to the problem

\angle N + \angle O =180\°

\angle O + \angle P = 180\°

\angle M + \angle P = 180\°

Which means,

\angle N + \angle O = \angle O + \angle P\\\angle N = \angle P

And,

\angle O + \angle P = \angle M + \angle P\\\angle O = \angle M

Therefore, the right answer is the last choice.


Apartial proof was constructed given that mnop is a parallelogram. by the definition of a parallelog
Mathematics
Apartial proof was constructed given that mnop is a parallelogram. by the definition of a parallelogram, mn ∥ po and mp ∥ no. using mp as a transversal, ∠m and ∠p are same-side interior angles, so they are supplementary. using no as a transversal, ∠n and ∠o are same-side interior angles, so they are supplementary. using op as a transversal, ∠o and ∠p are same-side interior angles, so they are supplementary. therefore, and because they are supplements of the same angle. which statements should fill in the blanks in the last line of the proof? ∠m
Step-by-step answer
P Answered by PhD
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
Apartial proof was constructed given that mnop is a parallelogram. by the definition of a parallelogram, mn ∥ po and mp ∥ no. using mp as a transversal, ∠m and ∠p are same-side interior angles, so they are supplementary. using no as a transversal, ∠n and ∠o are same-side interior angles, so they are supplementary. using op as a transversal, ∠o and ∠p are same-side interior angles, so they are supplementary. therefore, and because they are supplements of the same angle. which statements should fill in the blanks in the last line of the proof? ∠m
Step-by-step answer
P Answered by PhD
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


Apartial proof was constructed given that mnop is a parallelogram. by the definition of a parallelog
Mathematics
Apartial proof was constructed given that mnop is a parallelogram. by the definition of a parallelogram, mn ∥ po and mp ∥ no. using mp as a transversal, ∠m and ∠p are same-side interior angles, so they are supplementary. using no as a transversal, ∠n and ∠o are same-side interior angles, so they are supplementary. using op as a transversal, ∠o and ∠p are same-side interior angles, so they are supplementary. therefore, and because they are supplements of the same angle. which statements should fill in the blanks in the last line of the proof? ∠m
Step-by-step answer
P Answered by Specialist
Your answer is [d] ∠M ≅ ∠O; ∠N ≅ ∠P
Mathematics
Neil places £2000 in a bank account that pays 1.5% simple interest per year. How much interest will he earn in 6 years?
Step-by-step answer
P Answered by PhD

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
You can buy jars of the same jam in 2 sizes large jar:440g for £1.54 small jar:340g for £1.26 By considering the price per gram, work out which jar is the best value for money. Working must be shown
Step-by-step answer
P Answered by PhD
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
The last time Robert filled up his car with gas, he paid $24.50 for 7 gallons. This time, he needs 15 gallons. If the price is the same, how much will he pay?
Step-by-step answer
P Answered by PhD

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
An ice cream shop offers 5 different flavors of ice cream and 9 different toppings. How many choices are possible for a single serving of ice cream with one topping?
Step-by-step answer
P Answered by PhD

For 1 flavor there are 9 topping

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

No of choices= 5*9

=45 

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An online media service offers video and music downloads. Each download of a song costs $1. Each download of a video costs 5 times as much as the song download. You have a credit of $70. How many songs can you purchase after buying 12 videos?
Step-by-step answer
P Answered by PhD

The answer is in the image 

The answer is in the image 
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