If the arms of one angle are respectively parallel to the arms of another angle, then the two angles are

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neither equal nor supplementary

not equal but supplementary

equal but not supplementary

both equal and supplementary

answer is D.

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Detailed Solution

Concept:
In this question, we are given that arms of one angle are respectively parallel to the arms of another angle. Draw the figure of the same and using the condition of corresponding and co- interior angles check whether the angles are equal and supplementary or not.
Case 1:

https://lh3.googleusercontent.com/dGw6m1LsmCOxSZ1iOYlCg-WAHVLPMAbXMJ-zgSohj_AlF2EVg0EZtwPL2Im1B9TejubZJr6BM8832h4fcriJorCnyWOdw511eTTidtDHY7MRjX_sUchtkwbzGU5YDe1X8svS1z4Bc1I59XOhnie1Ig

Here,

(given)
As we know, corresponding angles are equal, if the transversal line intersects two parallel lines.
Therefore,

And

From equation (1) and (2) ,
We get

Case 2:

https://lh3.googleusercontent.com/S79ut4dsWEIVGa39TSmxNygdR_wojXSyTcE-I68U8YdyixEN3AiLqOfu6FOZJe1zIsfQjqUisMqtdw5qX6xJWWtscxkAD2EEW_658I39QxwhD90jZ8daLpgYe6YWRmg47MXyWEdRpkn6ZGcCPNUo9A

Again,

(given)
We’ll use the corresponding angles property.
Therefore,

Co- interior angles property – The sum of interior angles is equals to

degrees.
It implies that,

If the arms of the respective angles are equal, then the angles will be equal and supplementary.
Hence, the correct answer is option 4) both equal and supplementary

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