Question

In the given figure PQ is parallel to RS angle ACS =100, Determine angle BAC ,C and angle ABC.

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Answer 1

Answer:

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Answer 2

Answer:

∠ABC = 70°, ∠BAC = 30°, ∠C = 80°

Step-by-step explanation:

here, ∠ACS + ∠ACB = 180°                 by linear pair

     = 100° + ∠ACB = 180°

     = ∠ACB = 180° - 100°

     = ∠ACB = 80°

now, ∠ACB = ∠CAQ                PQ║RS and alternate interior angles

so, ∠CAQ = 80°

∵∠CAQ + ∠BAP + ∠BAC = 180°         by linear pair

= 80° + 70° +∠BAC = 180°

= ∠BAC = 180° - 150°

= ∠BAC = 30°

∴ ∠ABC + ∠BAC + ∠ACB = 180°          by angle sum property

= ∠ABC + 30° + 80° = 180°

= ∠ABC = 180° - 110°

= ∠ABC = 70°

hence, ∠ABC = 70°, ∠BAC = 30°, ∠C = 80°.

hope it help.