Answer:
See proof below
Step-by-step explanation:
From the given diagram, we can see that <2 and <3 lies on the same straight line, hence the sum of the angles is 180 degrees (supplementary)
<2 + <3 = 180 .... 1
Similarly. <1 and <2 are also supplementary angles
<1 + <2 = 180 .... 2
Subtract 1 from 2;
<3 - < 1 + <2 - <2 = 180 - 180
<3 - <1 +0 = 0
<3 - <1 = 0
Add <1 to both sides
<3 - <1 + <1 = 0+<1
<3 = <1 (Proved!)
This shows that <3 and <1 are equal
We can also conclude that <3 and <1 are vertically opposite angles and vertically opposite angles are equal
