Question

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Answer 1

Given: AB║CD and  BC║DE

To find: values of x and y

3x° = 105°  (Since AB║CD, the vertically opposite angles are equal)

x° = 105°/3

x° = 35°

105° = ∠CDE (Since BC║DE, the vertically opposite angles are equal)

24° + ∠CDE + y° = 180° (Angle Sum Property)

24° + 105° + y° = 180°

129° + y° = 180°

y° = 180° - 129°

y° = 51°

Therefore x = 35° and y = 51°

Hope it helps :)

Answer 2

Hey NIkshItha23 , Here's your matter

Given :- DE is parallel to BC and AB us parallel to CD

Angle ABC = 3x° , Angle BCD =105° , Angle DCE =24° ,Angle DEC = y°

To find :- x and y

As DE is parallel to BC (Given)

Y = Angle ACB {Corresponding angles} - Eq.1

Now , By given and eq.1 , we obtain,

y + 105° +24° = 180° {linear pair}

y = 180-105-24

y=180-129

y = 51

Now,Angle BCA = y = 51°

AB is parallel to CD {Given}

Angle DCE = Angle BAC (corresponding angles)

Angle BAC =24°

Now Angle BAC + Angle BCA + 3x =180° ( angle sum property)

24+51+3x =180

75+3x =180

3x =180-75=105

x=105/3=35

Conclusion y is 51 and x is 35

Thanks

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VATSALYA