Identify the incorrect statement.

  1. π‘šβˆ 2β€ˆ + π‘šβˆ 3β€ˆ = 180Β°
  2. ∠3β€ˆ β‰… β€ˆβˆ 7
  3. ∠3β€ˆ β‰… β€ˆβˆ 5
  4. π‘šβˆ 1β€ˆ + π‘šβˆ 3β€ˆ = β€ˆ180Β°


Use option checking method and determine whether each statement is true or false using a valid argument .If the option is incorrect /false then that option is the answer.Β 

The correct answer is: π‘šβˆ 1β€ˆ + π‘šβˆ 3β€ˆ = β€ˆ180Β°

    Explanation :-
    a. π‘šβˆ 2β€ˆ + π‘šβˆ 3β€ˆ = 180Β°
    True, As lines m and l are parallel then the sum of interior angles on the same side of the transversal is 180Β°.Angle 2 and angle 3 are interior angles lying on the same side of the transversal.
    b. ∠3β€ˆ β‰… β€ˆβˆ 7
    True,as angle 3 and angle 7 are alternate angles to transversal and interior angles to the parallel lines they both are alternate interior angles. As, alternate interior angles are equal ∠3β€ˆ β‰… β€ˆβˆ 7.
    c. ∠3β€ˆ β‰… β€ˆβˆ 5
    True, both angles 3 and 5 lie on the opposite angles at the intersection line l and t.
    They will be vertically opposite angles. As, vertically opposite angles are equal then ∠3β€ˆ β‰… β€ˆβˆ 5.
    d. π‘šβˆ 1β€ˆ + π‘šβˆ 3β€ˆ = β€ˆ180Β°
    False, angle 1 and angle 3 are the angles with corresponding positions at the different vertices. So, angles 1 and 3 are corresponding angles. As, corresponding angles are equal then ∠1β€ˆ β‰… β€ˆβˆ 3 but not π‘šβˆ 1β€ˆ + π‘šβˆ 3β€ˆ = β€ˆ180Β°.