Question

In the given figure, if CP || DQ, then the measure of x is

Options

• 130°

•  105°

• 175°

• 125°

Answer 1

Let us extend PC to meet AB at point O.

It is given that BQ || PO.

Thus,∠QBOand ∠AOP are corresponding angles. Therefore,

 ∠AOP =  ∠QBO

Given that ∠QBO = 150°, then we have:

 ∠AOP = 105V

Or, 

∠AOC =105°

Also, in ΔAOC, exterior angle is equal to the sum of the interior opposite angles, therefore,

 x =  ∠AOC + ∠COA

 x = 105° + 25°

 x = 130°