Question

In the given figure, $PQ=PR=PS$. Is $\angle Q={38}^o$, find the value of $x$.

• A. $120$
• B. $125$
• C. $142$
• D. $130$

Answer 1

Answer: (C)

$142$

In $△PQR$

$P+Q+R=180\Rightarrow R=180-(P+Q)=180-(90+38)$

$\Rightarrow R={52}^{\circ }$

In $△RSP$

$S+P+R=180\Rightarrow S=180-(P+R)=180-(90+52)$

$\Rightarrow S={38}^{\circ }$

$x+S=180\Rightarrow x=180-S=180-38$

$\Rightarrow x={142}^{\circ }$