Question

In the given figure, PQ || RS, ∠AEF = 95°, ∠BHS = 110° and ∠ABC = x°. Then the value of x is

(a) 15°

(b) 25°

(c) 70°

(d) 35°

Answer 1

In the given figure,

.

Also,and are the corresponding angles.

Then, according to the Corresponding Angles Axiom, which states:

If a transversal intersects two parallel lines, then each pair of corresponding angles are equal.

Therefore,

It is given that

Therefore,

Clearly, and form a linear pair, therefore, their sum must be supplementary.

Therefore,

On substituting in equation above, we get:

In ΔBHG:

We know that, in a triangle exterior angle is equal to the sum of the interior opposite angles. Therefore,

Substituting

and , we get :

Hence the correct choice is (b).