Question

In the adjoining figure if Ray BA is parallel to DE, angle C =50° and angle D=100°. Find the measure of the angle ABC.

pls tell step by step​

Answer 1

Answer:

Draw a line XY passing through point C and parallel to AB.

We have, AB∥DE and AB∥XY.

It is known that, if two lines in a plane are parallel to a third line in the plane, then those two lines are parallel to each other.

∴DE∥XY.

Since DE∥XY and DC is a transversal intersecting them at D and C, then

∠EDC+∠YCD=180∘  (Pair of interior angles on the same side of transversal are supplementary)

⇒100∘+∠YCD=180∘

∠YCD=180∘−100∘=80∘

Since, sum of all the angles on a straight line at a point is 180∘, then

∠XCB+∠BCD+∠YCD=180∘

⇒∠XCB+50∘+80∘=180∘

⇒∠XCB+130∘=180∘

⇒∠XCB=180∘−130∘=50∘

Since, AB∥XY and BC is a transversal intersecting them at B and C, then

∠ABC+∠XCB=180∘ (Pairs of interior angles on the same side of transversal are supplementary)

⇒∠ABC+50∘=180∘

⇒∠ABC=180∘−50∘=130°