In the adjoining figure Ray BA parallel Ray DE, angle C=50digere and angleD=100digere find m angle ABC
Answers
Step-by-step explanation:
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
ZEDC + ZYCD = 180° (Pairs of interior angles on the same side of transversal are supplementary)
⇒ 100 ° + ZYCD = 180 °
ZYCD = 180° - 100° = 80° - Since, sum of all the angles on a straight line at a point is 180°, then ZXCB+ ZBCD + <YCD = 180° = zXCB + 50° + 80° = 180°
→ zXCB + 130° = 180°
→ 2XCB = 180 ° - 130 ° = 50 °
Since, AB || XY and BC is a transversal intersecting them at B and C, then
ZABC + ZXCB = 180° (Pairs of interior angles on the same side of transversal are supplementary)
→ ZABC + 50° = 180°
→ <ABC = 180° - 50° = 130°
Hope this helps you.
:)
