Prove below?

Given: #angle 2# and #angle 3# are supplementary

Prove: #angle 1# and #angle 4# are supplementary

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1 Answer
May 18, 2018

See below.

Explanation:

We are given that #angle 2# and #angle 3# are supplementary, which means

[1] #angle 2 + angle 3 = 180^o#

We can use the vertical angle theorem to obtain

[2] #angle 4 = angle 2#

and

[3] #angle 1 = angle 3#

Now we substitute [2] and [3] into [1]

#angle 4+angle 1 = 180^o#

Which by definition means that #angle 4# and #angle 1# are supplementary.