m∠3 = 142°
Solution:
Line l and m are parallel.
Sum of the adjacent angles in a straight line is 180°.
⇒ 38° + m∠1 = 180°
⇒ m∠1 = 180° – 38°
⇒ m∠1 = 142°
∠1 and ∠3 are corresponding angles.
If two parallel lines are cut by a transversal, then the corresponding angles on the same side are congruent.
⇒ ∠1 ≅ ∠3
⇒ m∠1 = m∠3
⇒ m∠3 = 142°
Therefore m∠3 = 142°.
The value of ∠3 is 142 degree.
Given that, Lines L and M are parallel.
So that, [tex]\angle 6=38[/tex] (Vertically opposite angles are equal)
The Sum of internal angles on one side of transversal is equal to 180 degree
[tex]\angle5+\angle6=180[/tex]
[tex]\angle5+38=180\\\\\angle5=180-38=142[/tex]
Since, angle 3 and 5 are vertically opposite angles.
So that, [tex]\angle3=\angle5=142[/tex]
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