Question

In the given figure, if BP || CQ and AC = BC, then the measure of x is

(a) 20°

(b) 25°

(c) 30°

(d) 35°

Answer 1

In the given figure,and

We need to find the measure of x

Here, we draw a line RS parallel to BP, i.e

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

As,

Thus,

Now, and BA is the transversal, so using the property, “alternate interior angles are equal”

Similarly, and AC is the transversal

........(2)

Adding (1) and (2), we get

Also, as

Using the property,”angles opposite to equal sides are equal”, we get

Further, using the property, “an exterior angle is equal to the sum of the two opposite interior angles”

In ΔABC

Thus,

Therefore, the correct option is (c).