Question

In the given diagram(not drawn to scale), $PQ$ and $RS$ are straight lines, which of the following statements is true?

• A. $\angle f=\angle d$
• B. $\angle c=\angle e$
• C. $\angle a+\angle b=\angle f+\angle e$
• D. $\angle b+\angle c=\angle e+\angle f$

Answer 1

The correct option is D $\angle b+\angle c=\angle e+\angle f$

Given that $PQ$ and $RS$ are two intersecting lines intersect at point $O$.

$\angle ROQ=\angle POS$ .....Vertical opposite angles are equal.

$\angle ROQ=\angle b+\angle c$ and

$\angle POS=\angle e+\angle f$

$\Rightarrow \angle b+\angle c=\angle e+\angle f$