Question

In the given figure, AB || CD ∠EAB=105∘ ∠AEC=25∘ and ∠ECD=x∘. Find the value of x.

Answer 1

Therefore the value of 'x' is 130°.

Given:

AB || CD, ∠EAB=105∘, ∠AEC=25∘ and ∠ECD=x∘.

To Find:

The value of 'x'.

Solution:

This problem can be solved easily as shown below.

Given that: AB║CD, ∠EAB=105∘, ∠AEC=25∘ , and ∠ECD=x∘.

Now draw EF║CD and also EF║AB so AE is a Transverse line.

Let ∠DEF be 'y°'.

⇒ ∠EAB + ∠AEF = 180°

⇒ 105° + 25° + y° = 180°

⇒ y = 180° - 130° = 50°

Now EF║CD then CE is a transverse line.

∴ ∠x + ∠y = 180°

⇒ ∠x + 50°= 180°

⇒ ∠x  = 130°

Therefore the value of 'x' is 130°.

#SPJ1