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The properties or relationship between the angles m∠1, m∠2, and m∠3 can be used to determine the statement that must be true
The correct option that gives the statement that must be true to prove that m∠1 + m∠2 + m∠3 = 180°, is the first option
A. m ║ n
Reason:
Which statement must be true to prove that m∠1 + m∠2 + m∠3 = 180°?
A. m ║ n
B. m∠1 + m∠2 = 180° - m∠3
C. m∠1 + m∠2 = 90°
D. m∠1 = m∠2 = m∠3
Given that m∠1 + m∠2 + m∠3 = 180°, we have;
m∠ACD + m∠2 + m∠3 = 180° by angles on a straight line
Therefore;
m∠ACD = m∠1 by addition property of equality
m∠ACD ≅ m∠1 by definition of congruency
m∠ACD and m∠1 are alternate interior angles formed between lines m and n and their common transversal AC
Which gives;
m ║ n, by alternate interior angles theorem which states that alternate interior formed between parallel lines are congruent
Therefore;
The statement that must be true to prove that m∠1 + m∠2 + m∠3 = 180° is m ║ n
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