Question

In the figure, $\Delta OPR\sim \Delta OSK,\angle POS={125}^o$ and $\angle PRO={70}^o$. Find the values of $\angle OKS$ and $\angle ROP$.

• A. $\angle ROP={50}^o$ and $\angle OKS={80}^o$
• B. $\angle ROP={55}^o$ and $\angle OKS={70}^o$
• C. $\angle ROP={75}^o$ and $\angle OKS={15}^o$
• D. $\angle ROP={45}^o$ and $\angle OKS={45}^o$

Answer 1

The correct option is B $\angle ROP={55}^o$ and $\angle OKS={70}^o$

Given:

$\Delta OPR\sim \Delta OSK$

$\angle POS={125}^o$

$\angle PRO={70}^o$

To find:

$\angle OKS$

$\angle ROP$

Sum of supplementary angles is ${180}^o$

$\angle POS+\angle ROP={180}^o$

${125}^o+\angle ROP={180}^o$

$\angle ROP={55}^o$

$\angle OKS=\angle PRO\because \Delta OPR\sim \Delta OSK$

$\angle OKS={70}^o$