In the adjoining figure AB|| CD and CD || EF. Also, EA ⊥ AB. If ∠BGD = 62°, then the value of w is:

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Correct option is A

Given :

AB|| CD and CD || EF. 

EA ⊥ AB. If ∠BGD = $$62^\circ$$​  

Concept Used: 

For a parallel line which has transversal line, 

Corresponding angles are equal. 

Alternate Interior Angles are equal 

Alternate Exterior Angles are equal

The pairs of interior angles on the same side of the transversal are supplementary.

Solution: 

From the figure,

$$\angle A = \angle C = 90^\circ$$  (corresponding angle because AB parallel CD.

$$\angle DGB = \angle EGC$$  = $$62^\circ$$ (vertically opposite angle)

consider triangle $$\triangle$$​ECG

 $$\angle E + \angle G + \angle C = 180^\circ$$​

$$62^\circ + 90^\circ + w^\circ = 180^\circ$$ 

$$w^\circ = 28^\circ$$