Question

In the given figure; AE || BD, AC || ED and AB = AC. Find ∠a, ∠b and ∠c.

Answer 1

Let P and Q be the points as shown below: 

Given:
∠PDQ = 58°
∠PDQ = ∠EDC = 58° .....[ Vertically opp . angles ]
∠EDC = ∠ACB =58° ........[ Corresponding angles  ∵ AC || ED ]

In  ΔABC,
AB = AC .......[ Given ]
∴ ∠ACB = ∠ABC = 58° ......[angels opp. to equal sides are equal]
Now, 
∠ACB + ∠ABC+ ∠BAC = 180°
⇒ 58° + 58° + a = 180°
⇒ a = 180° − 116°
⇒ a = 64°
Since AE || BD and AC is the transversal. 
∠ABC = b .......[ Corresponding angles ]
∴ b = 58°

Also since AE || BD and ED is the transversal 
∠EDC = c  .......[ Corresponding angles ] 
∴ c = 58°