Answer :

110°

Concept to be used :

• Exterior angle property of a triangle : The exterior angle of a triangle is equal to the sum of its opposite interior angles.

• When two parallel lines are cut by a transversal, then

1. Corresponding angles are equal.
2. Alternate interior angles are equal.
3. Alternate exterior angles are equal.
4. Co-interior angles are equal supplementary, i.e. their sum is 180°.

Solution :

• Given : AB || CD, ∠ABE = 130°, ∠BED = 20°
• To find : ∠EDC = ?

Now,

Using exterior angle property of a triangle in ∆BEF,

We have, ∠BEF + ∠EFB = ∠ABE

→ ∠BED + ∠EFB = ∠ABE (°•°∠BEF = ∠BED)

→ 20° + ∠EFB = 130°

→ ∠EFB = 130° - 20°

→ ∠EFB = 110°

Now,

AB || CD and ED is transversal, thus

→ ∠EDC = ∠EFA

(°•° Corresponding angles are equal)

→ ∠EDC = ∠EFB (°•°∠EFA = ∠EFB)

→ ∠EDC = 110°

Hence, ∠EDC = 110°

Answer:

• hope this helps you
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