Question

Which statement must be true to prove m angle<1+m angle m<2+m<3=180^ ? 2 3 B A A m angle1+m angle2=180^ -m angle3; m angle1+m angle2=90^; m angle1=m angle2=m angle3

Answer 1

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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