Question

If the sum of adjacent angles is 180 then their non common arms are two opposite rays​

Answer 1

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Answer 2

Step-by-step explanation:

It is given in the question that the sum of two

adjacent angles is 180 then we have to prove that their non-common arms are two opposite rays.

Basically rays means, straight line having no end point. To show that two non-common arms are opposite to each other, we will first assume that they are not opposite to each other.

According to the question, we have

<ACD+ <BCD = 180°.... (i)

Also, we have assumed that CA is not opposite to CB. We have assumed that CE is opposite to

CA also sum of ACD and <ECD is equal

to 180°, we get

<ACD+<ECD = 180°.

(ii)

On subtracting equation 1 and equation 2, we get,

(<ACD + <BCD) - (<ACD+<ECD) = 180°

solving further, we get

<BCD-<ECD=0 therefore,

<BCD= <ECD.... (iii)

But we know that CB and CE on the same side of CD, therefore, equation 3 is only possible if CE and CB coincide, and we know that CE is opposite to CA, thus CB is also opposite to CA. Hence proved.