In the given figure, DE is parallel to BC. Angle ABC = 40 degrees. Angle ADE = 130 degrees. What is the value (in degrees) of angle BAD?

Correct option is C

Given:

DE ∥ BC

∠ABC = 40°

∠ADE = 130°

Find ∠BAD

Concept Used:

Parallel line angle properties

Triangle angle relation

Formula Used:
Angles on a straight line = 180°
Sum of angles in a triangle = 180°

Solution:

Since DE ∥ BC, the angle between AD and BC equals the angle between AD and DE.

Given:
∠ADE = 130°

Therefore, the interior angle between AD and the horizontal line BC is:

180° − 130° = 50°

Now at B:

∠ABC = 40°

So in triangle formed by extending the directions from B and D toward A:

At A, the angle is the sum of inclinations of AB and AD with the horizontal line:

∠BAD = 40° + 50° = 90°

Hence,

∠BAD = 90°