Question

If m∠7 = 55°, which of the following statements are true? Select all that apply. There are two horizontal parallel lines are cut by a transversal. The top left angle is denoted by 1 when transversal line makes an angle with upper horizontal line. The supplementary angle of angle 1 (which is top right angle) is denoted by 2 and opposite angle is denoted by 4. The remaining angle is denoted by 3. The corresponding angle of 1 is denoted by 5 and the corresponding angle of 2 is denoted by 6. The opposite angle of 5 is denoted by 8 and opposite angle of 6 denoted by 7. A. m∠6 = 55° B. m∠5 = 135° C. m∠1 + m∠4 = 250° D. m∠1 + m∠6 = m∠7 + m∠4

Answer 1

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.