Answer:
The true statements are;
A. m∠6 = 55°
C. m∠1 + m∠4 = 250°
D. m∠1 + m∠6 = m∠7 + m∠4
Step-by-step explanation:
The given information are;
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
Similarly, the angles formed by the transversal and the lower horizontal parallel line are (starting from the top left and moving in clockwise direction) = 5, 6, 8, 7
Therefore, we have;
m∠7 ≅ m∠6 (Vertically opposite angles are congruent)
∴ m∠6 = m∠7 = 55°
m∠6 = 55° which corresponds with option A.
m∠5 + m∠6 = 180° (The sum of angles on a straight line)
∴ m∠5 = 180° - m∠6 = 180° - 55° = 125°
m∠5 = 125°
m∠1 ≅ m∠5 (Corresponding angles)
∴ m∠1 = m∠5 = 125°
m∠1 ≅ m∠4 (Vertically opposite angles)
∴ m∠1 = m∠4 = 125°
∴ m∠1 + m∠4 = 125° + 125° = 250°
m∠1 + m∠4 = 250° which corresponds with option C.
m∠1 ≅ m∠4 (Vertically opposite angles)
m∠6 ≅ m∠7 (Vertically opposite angles)
∴ m∠1 + m∠6 = m∠7 + m∠4 (Transitive property) which corresponds with option D.
