The measures of the missing angles are: m∠1 = m∠3 = m∠5 = m∠7 = m∠9 = m∠11 = 76°, m∠2 = m∠4 = m∠6 = m∠8 = m∠10 = m∠12 = 104°
Find the measure of each missing angle:
Identify the corresponding angles: Since lines a, b, and c are parallel, we have corresponding angles and alternate interior angles.
Corresponding angles: ∠1 and ∠9, ∠2 and ∠10, ∠3 and ∠11, and so on.
Alternate interior angles: ∠1 and ∠5, ∠2 and ∠6, ∠3 and ∠7, and so on.
Use the fact that corresponding angles are congruent: Since a || b || c, we know that corresponding angles are congruent. Therefore:
m∠1 = m∠9 = 76°
m∠2 = m∠10 = 180° - 76° = 104°
m∠3 = m∠11 = 76°
and so on.
Use the fact that alternate interior angles are congruent: Similarly, since a || b || c, we know that alternate interior angles are congruent. Therefore:
m∠1 = m∠5 = 76°
m∠2 = m∠6 = 104°
m∠3 = m∠7 = 76°
and so on.