Answer: Since lines l and m are parallel, we can use the fact that corresponding angles are congruent. Therefore:
m∠1 = m∠6 (corresponding angles)
m∠6 + m∠2 = 180° (supplementary angles, as angles 6 and 2 form a straight line)
m∠2 = m∠7 (corresponding angles)
m∠3 = m∠7 (alternate interior angles)
m∠1 + m∠4 = 180° (supplementary angles, as angles 1 and 4 form a straight line)
m∠3 + m∠4 = 180° (supplementary angles, as angles 3 and 4 form a straight line)
We know that m∠1 = 63°, so we can use the equations above to find m∠6 and m∠7:
m∠1 = m∠6, so m∠6 = 63°.
m∠6 + m∠2 = 180°, so m∠2 = 180° - m∠6 = 180° - 63° = 117°.
m∠2 = m∠7, so m∠7 = 117°.
m∠3 = m∠7, so m∠3 = 117°.
m∠1 + m∠4 = 180°, so m∠4 = 180° - m∠1 = 180° - 63° = 117°.
m∠3 + m∠4 = 180°, so m∠3 + 117° = 180°, which means m∠3 = 63°.
Therefore, the measures of the angles are:
m∠1 = 63°
m∠2 = 117°
m∠3 = 63°
m∠4 = 117°
m∠6 = 63°
m∠7 = 117°
Explanation: