Question

Complete the paragraph proof

Answer 1

Two angles are supplementary if their sum is a straight angle, which means that the sum of their measures is equal to 180°.

Therefore if you have ∡1 and ∡2 that are supplementary, it means that that measure of ∡1 plus the measure of ∡2 is equal to 180°, or M∡1+M∡2=180°;

Similarly, the measure of ∡2 plus the measure of ∡3 is equal to 180°, or M∡2+M∡3=180°

Since they are equal to the same quantity (180°), they must be equal to each other: M∡1+M∡2=M∡2+M∡3

You can subtract the measure of ∡2 from both sides: 
M∡1+M∡2-M∡2=M∡2+M∡3-M∡2
which brings to:
M∡1=M∡3

If two angles have the same measure they are said congruent, therefore ∡1 is congruent to ∡3.