Applying the linear pair theorem and the sum of interior angles of hexagon, we have:
Angle 7 = 92°
Angle 1 = 107°
What is the Linear Pair Theorem?
According to the linear pair theorem/postulate, when two angles lie on a straight line, the sum of their measures equals 180 degrees.
Angle 7 lie on a straight line with 88°, therefore, applying the linear pair theorem, we have:
Angle 7 + 88 = 180
Subtract both sides by 88
Angle 7 + 88 - 88 = 180 - 88
Angle 7 = 92°
Also, using the linear pair theorem, we have:
Angle 5 = 180 - 64
Angle 5 = 116°
Angle 3 = 180 - 57
Angle 3 = 123°
Sum of interior angles of hexagon equals 720°, therefore:
Angle 1 + angle 3 + angle 5 + angle 7 + 118 + 164 = 720°
Plug in the known values
Angle 1 + 123 + 116 + 92 + 118 + 164 = 720
Angle 1 + 613 = 720
Subtract both sides by 613
Angle 1 + 613 - 613 = 720 - 613
Angle 1 = 107°
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