Question

In the given figure AB ||DE find angle ACD when angle BAc=30 and angle CDE=40

Answer 1

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Answer 2

Answer:

∠DCA  = 70°

Step-by-step explanation:

Since AB ║ DE, ∠BAE = ∠DEB = 30°....  Alternate angles

Similarly, ∠EDB = ∠DBA = 40°

In ΔACB, ∠A + ∠B + ∠ACB = 180° ... Sum of angles of a triangle.

30° + 40° + ∠ACB = 180°

70° + ∠ACB = 180°

∠ACB = 180° - 70°

∠ACB = 110°

∠DCE = ∠ACB = 110°   ....  Vertically opposite angles.

∠DCA  + ∠ACB = 180°

∠DCA  + 110° = 180°

∠DCA   = 180° - 110°

∠DCA  = 70°