Answer/Step-by-step explanation:
The diagram given shows a transversal line crossing two parallel lines, thereby forming different angles.
Given that m∠ 6 = 142°, the following are the measures of the missing angles that are labelled with numbers, with the reasons given in parentheses:
a. m∠1 = m∠6 (both are vertical angles and are therefore congruent).
Therefore, m∠1 = 142°
b. m∠2 = 180° - 142° (∠2 and ∠6 are supplementary angles)
m∠2 = 38°
c. m∠3 = m∠1 (they are corresponding angles, and are therefore congruent).
Therefore, m∠3 = 142°
d. m∠4 = m∠2 (they are corresponding angles, and are therefore congruent).
Therefore, m∠4 = 38°
e. m∠5 = m∠2 (both are vertical angles and are therefore congruent).
Therefore, m∠5 = 38°
f. m∠7 = m∠4 (both are vertical angles and are therefore congruent).
Therefore, m∠7 = 38°
g. m∠8 = m∠6 (they are corresponding angles, and are therefore congruent).
Therefore, m∠8 = 142°