Based on the definition of supplementary angles and properties for algebraic handling, we conclude that the measure of angle 6 is equal to 108°.
What is the measure of an angle generated by two non-parallel lines?
According to the Euclidean geometry, a line crossed by a non-parallel line generates four pairs of supplementary angles. Two angles are supplementary if and only if the angles are adjacent to each other and the sum of their measures is equal to 180°.
Then, we know that the mathematical model is m ∠ 6 + m ∠ 7 = 180° = 72° + m ∠ 7 = 180°. Thus, m ∠ 7 = 108°. Based on the definition of supplementary angles and properties for algebraic handling, we conclude that the measure of angle 6 in the system generated by two non-parallel lines is equal to 108°.
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