Answer :

35; ∠2 and ∠4 are alternate interior angles, so m∠2 = m∠4.

What is alternate interior angles?

  • Two angles that are on the interior of and, but on different sides of the transversal, are said to be alternate interior angles.
  • The alternate interior angles theorem states that the alternate interior angles must be congruent if two parallel lines are cut by a transversal.

Given

           m∠4=35

From the image given, angle 2 and angle 4 lie on opposite side of the line that intercepts the two parallel lines, AB and CD. Angle 2 and angle 4 both lie within the parallel lines. Therefore, ∠2 and ∠4  are alternate interior angles.

Thus:

m ∠2 = m∠4 (alternate interior angles theorem)

since m∠4 = 35°

therefore m∠2 = 35°

Learn more about alternate interior angles

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