Answer:
The accurate assertions include:
A. m∠6 = 55°
C. m∠1 + m∠4 = 250°
D. m∠1 + m∠6 = m∠7 + m∠4
Step-by-step clarification:
The provided information is as follows:
m∠7 = 55°
The angles formed by the transversal and the upper horizontal parallel line are (starting from the top left and moving in clockwise direction) 1, 2, 4, 3
Likewise, the angles from the transversal and the lower horizontal parallel line are (starting from the top left and going clockwise) 5, 6, 8, 7
Consequently, we have;
m∠7 ≅ m∠6 (Vertically opposite angles are equal)
Thus, m∠6 = m∠7 = 55°
m∠6 = 55°, which aligns with option A.
m∠5 + m∠6 = 180° (The sum of angles on a straight line)
So, m∠5 = 180° - m∠6 = 180° - 55° = 125°
m∠5 = 125°
m∠1 ≅ m∠5 (Corresponding angles)
Thus, m∠1 = m∠5 = 125°
m∠1 ≅ m∠4 (Vertically opposite angles)
Therefore, m∠1 = m∠4 = 125°
Thus, m∠1 + m∠4 = 125° + 125° = 250°
m∠1 + m∠4 = 250°, which corresponds to option C.
m∠1 ≅ m∠4 (Vertically opposite angles)
m∠6 ≅ m∠7 (Vertically opposite angles)
Thus, m∠1 + m∠6 = m∠7 + m∠4 (Transitive property), which matches option D.
