Question

In the figure , BD।।CE . Find x and y

Answer 1

angle DBA =70°(vetically opposite angles)
angle BDA=180°-120°(linear pair)
=60°
angle DBA+BDA+X=180° (angle sum property of a traingle)
70°+60°+X=180°
130°+X=180°
X=180°-130°
X=50°
Now,
angle BDE=180°-120°(Linear pair)
=60°
then,
angle Y =angle BDE(corresponding angles)
60°=60°

Answer 2

In the Figure We can notice that the Angle where Letter D is Present and Angle 120 make a Linear Pair.

⇒ 120° + Angle at Letter D = 180°

⇒ Angle at Letter D = 180° - 120°

⇒ Angle at Letter D is 60°

As BD and CE are Parallel lines :

The Angle at Letter D should be Equal to Angle at y, Because they are Corresponding angles.

⇒ y = 60°

Now let us look at Triangle ADB :

We can notice that the Angle Opposite to Letter D is the one of the Vertex of Triangle ADB.

Angle Opposite to Letter D should be Equal to Angle at Letter D, Because they are Vertically Opposite angles.

⇒ Angle Opposite to Letter D = 60°

Angle Opposite to 70° should be Equal to Angle 70°, Because they are Vertically Opposite angles.

⇒ Angle Opposite to 70° = 70°

We know that Sum of Angles in a Triangle = 180°

Angle x + Angle Opposite to D + Angle Opposite to 70° = 180°

Angle x + 60° + 70° = 180°

Angle x + 130° = 180°

Angle x = 180° - 130°

Angle x = 50°