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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
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