Let's remember some angle pair rules:
-> Co-Interior angles add up to 180º.
-> Alternating angles are equal.
-> Corresponding angles are equal.
-> Vertically opposite angles are equal.
-> Angles on a straight line add up to 180º.
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Knowing that, and knowing Angle 6 = 102º, you can easily find any of the 7 angles.
I will skip angle 1 for now, you'll understand why.
Angle 2 and Angle 6 are Corresponding, so Angle 2 must be 102º.
Angle 3 is Vertically Opposite to Angle 2, so Angle 3 must be 102º.
Angle 4 is Co-Interior to Angle 6, so we calculate it this way:
[tex]A4=180-A6\\A4=180-102\\A4=78[/tex]
Angle 4 must be 78º.
Angle 1 is Vertically Opposite to Angle 4, so it must be 78º.
Angle 5 is Alternating to Angle 4, so Angle 5 must be 78º.
Angle 7 and Angle 5 are On A Straight Line, so Angle 7 is calculated this way:
[tex]A7=180-A5\\A7=180-78\\A7=102[/tex]
Angle 7 must be 102º.
Angle 8 is Vertically Opposite to Angle 5, so it must be 78º.
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I wrote some parts in bold so you can refer to the rules I wrote above.
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In summary:
Angles 1, 4, 5, and 8 = 78º
Angles 2, 3, 6 and 7 = 102º
