Maths-
General
Easy

Question

Identify the incorrect statement.

  1. 𝑚∠2  + 𝑚∠3  = 180°
  2. ∠3  ≅  ∠7
  3. ∠3  ≅  ∠5
  4. 𝑚∠1  + 𝑚∠3  =  180°

hintHint:

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. 

The correct answer is: 𝑚∠1  + 𝑚∠3  =  180°


    Explanation :-
    a. 𝑚∠2  + 𝑚∠3  = 180°
    True, As lines m and l are parallel then the sum of interior angles on the same side of the transversal is 180°.Angle 2 and angle 3 are interior angles lying on the same side of the transversal.
    b. ∠3  ≅  ∠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 ∠3  ≅  ∠7.
    c. ∠3  ≅  ∠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 ∠3  ≅  ∠5.
    d. 𝑚∠1  + 𝑚∠3  =  180°
    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 ∠1  ≅  ∠3 but not 𝑚∠1  + 𝑚∠3  =  180°.
     

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