Question

In the given figure, AB and CD are parallel lines and transversal EF intersects them at P and Q respectively. If ∠APR = 25°, ∠RQC = 30° and ∠CQF = 65°, then

(a) x = 55°, y = 40°

(b) x = 50°, y = 45°

(c) x = 60°, y = 35°

(d) x = 35°, y = 60°

Answer 1

In the given figure,,,and

We need to find the value of x and y

Here, we draw a line ST parallel to AB, i.e

Also, using the property, “two lines parallel to the same line are parallel to each other”

As,

Thus,

Now, and EF is the transversal, so using the property, ”alternate interior angles are equal”, we get,

Similarly,and EF is the transversal

.......(2)

Adding (1) and (2), we get

Further,FPE is a straight line

Applying the property, angles forming a linear pair are supplementary

Also, applying angle sum property of the triangle

In ΔPRQ

Thus,

Therefore, the correct option is (a).