Question

The sides BA and DC of the parallelogram ABCD are produced as shown in figure then which of the following option is correct?

• A. $\angle a=\angle x+\angle y$
• B. $\angle a=\angle b=\frac{1}{2}(\angle x+\angle y)$
• 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, AB || DC

$\therefore \angle a=\angle x\cdots \left(1\right)$ [Alternate Interior Angles]
And, $\angle b=\angle y\cdots \left(2\right)$ [Alternate Interior Angles]
Adding (1) and (2), we get;
$\angle a+\angle b=\angle x+\angle y$