Question

If $\angle P={52}^o$ and $\angle PQO={64}^o$. If $QO$ and $RO$ are bisectors of $\angle PQR$ and $\angle PRQ$ respectively, then the value of $\angle x$ and exists but value of $\angle y$ does not exists

• A. True
• B. False

Answer 1

The correct option is A True

$\angle OQP=\angle OQR={64}^{\circ }$

$\angle ORQ=\angle ORP=y$

$(\because QO\&ROareangularbisectors)$

$In△PQR$

$\angle P+\angle Q+\angle R={180}^{\circ }$

$\angle P+(\angle PQO+\angle OQR)+(\angle ORQ+\angle ORP)={180}^{\circ }$

${52}^{\circ }+\left({64}^{\circ }{+64}^{\circ }\right)+(y+y)={180}^{\circ }$

$2y=180-(128+52)$

$2y=0$

$y=0^{\circ }$

$\therefore ydoesnotexist$

$In△OQR$

$\angle QOR+\angle OQR+\angle ORQ={180}^{\circ }$

$x+64+y={180}^{\circ }$

$x+y={180}^{\circ }{-64}^{\circ }$

$x={116}^{\circ }$

$Wedogetavalueofxbut△QORcannotexist(\because y=0^{\circ })$

$A)True$