Question

In the given figure, AB || CD. If ∠EAB = 50° and ∠ECD = 60°, then ∠AEB = _____.

• A. ${50}^{\circ }$
• B.
  ${60}^{\circ }$
• C.
  ${70}^{\circ }$
• D.
  ${55}^{\circ }$

Answer 1

The correct option is C

${70}^{\circ }$

AB ∥ CD and BC is transversal.
∴ ∠ABE = ∠ECD = 60°
[Alternate interior angles]

In ∆ABE, we have:
∠EAB + ∠ABE + ∠AEB = 180°
[Angle sum property of a triangle]

⇒ 50° + 60° + ∠AEB = 180°
⇒ ∠AEB = 70°