1.

AB||DC and AD||BC if DAB is 75 find the measures of a b cgive answer by step by step​

Answer»

AB ║ DC      and      AD ║ BCand, ∠DAB = 75°Solution:-Here, AD ║ BC  and  AB is transversal∵ CONSECUTIVE interior angles are supplementary∴ ∠DAB + ∠ABC = 180°              [ AD ║ BC and they are Consecutive interior angles ]so, 75° + ∠ABC = 180°⇒ ∠ABC = 180° - 75°⇒ ∠ABC = a = 105°Now, AB ║ DC  and  BC is transversal∵ Consecutive interior angles are supplementary∴ ∠DCB + ∠ABC = 180°               [ AB ║ DC and they are Consecutive interior angles ]so, ∠DCB + 105° = 180°⇒ ∠DCB = 180° - 105°⇒ ∠DCB = b = 75°Now, AD ║ BC  and  DC is transversal∵ Alternate interior angles are Equal in measure∴ ∠DCB = ∠EDC             [ AD ║ BC and they are Alternate interior angles ]⇒ ∠EDC = C = 75°Hence, a = 105°  and  b = c = 75°Some important TERMS:-When two parallel lines intersected by a transversal then:-Alternate interior angles are equal.Alternate EXTERIOR angles are equal.Corresponding angles are equal.Consecutive interior angles are supplementary.Vertically opposite angles are equal.



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