Question

The sides NM and PO of the parallelogram MNOP are produced as shown in the figure given below. Which of the following statements is correct?

• A. $\angle a=\angle x+\angle y$
• B. $\angle a=\angle b=(\angle x+\angle y)$
• C. $\angle y=\angle a-\angle b$
• D. $\angle a+\angle b=\angle x+\angle y$

Answer 1

The correct option is D $\angle a+\angle b=\angle x+\angle y$

In the given figure, MN || PO


$\therefore \angle a=\angle x\cdots \left(1\right)\text{[Alternate Interior Angles]}$

And,
$\angle b=\angle y\cdots \left(2\right)\text{[Alternate Interior Angles]}$

So, by adding (1) and (2), we get:

$\angle a+\angle b=\angle x+\angle y$