Question

Lines $PQ$ and $RS$ intersect at $O$. If $\angle POS=2\angle SOQ$ then the four angles at $O$ are

• A. ${30}^o,{30}^o,{120}^o,{180}^o$
• B. ${60}^o,{60}^o,{120}^o,{120}^o$
• C. ${60}^o,{90}^o,{90}^o,{120}^o$
• D. ${30}^o,{60}^o,{90}^o,{180}^o$

Answer 1

Answer: (B)

${60}^o,{60}^o,{120}^o,{120}^o$

$x+2x=180\left(linearpair\right)\Rightarrow x={60}^o\Rightarrow \angle SOP={120}^o$
$\therefore \text{four angle are at O}are{60}^o,{60}^o,{120}^o,{120}^o$