Answer:
Explanation:
Remark
If you find < 3 first, that will give you angle 5 by alternate interior angles. <5 and <7 are equal by vertically opposite angles.
Solution
<3 + <2 = 180o these two angles are on the same straight line.
<3 + 83 = 180o Subtract 83 from both sides
<3 = 180 - 83
<3 = 97
As per the remark <3 = <5 by alternate interior angles.
<5 = 97
<7 = 97 Vertically opposite angles are equal
Note
There are 4 angles that are equal to 83 and 4 angles that are equal to 97
83: angles 2 4 6 and 8
97: angles 1 3 5 and 7
No other values for this diagram are possible and these are always the result.