Question

In the given diagram, $ABCD$ is a rhombus, $AEC$ and $BED$ are straight lines.
$p+q+r+s+t=?$

• A. ${200}^o$
• B. ${270}^o$
• C. ${360}^o$
• D. ${540}^o$

Answer 1

Answer: (B)

${270}^o$

In the rhombus $ABCD$
$\angle A+\angle B+\angle C+\angle D={360}^o$
$\Rightarrow$ $\frac{\angle A}{2}+\frac{\angle B}{2}+\frac{\angle C}{2}+\frac{\angle D}{2}={180}^o$
$\Rightarrow$ $p+q+t+s={180}^o$
($\therefore$ Diagonals $AC$ and $BD$ of rhombus $ABCD$ bisect the angles $A,C$ and $B,D$ respectively)
Also, diagonals of a rhombus are perpedicular to each other so $r={90}^o$
$\therefore$ $p+q+r+s+t={180}^o+{90}^o={270}^o$