Question

In fig sides QP and RQ of $\Delta$PQR are produced to .the points S and T respectively. If $\angle SPR={105}^{\circ }\angle PQT={110}^{\circ }$ then find $\angle PRQ$.

• A. ${35}^o$
• B. ${70}^o$
• C. ${105}^o$
• D. ${140}^o$

Answer 1

The correct option is A ${35}^o$

$\angle SPR+\angle RPQ=180$ (Angles on a straight line)
$105+\angle RPQ=180$
$\angle RPQ={75}^{\circ }$
$\angle TQP+\angle PQR=180$ (Angles on a straight line)
$110+\angle PQR=180$
$\angle PQR={70}^{\circ }$
Now, in $△PQR$
$\angle PQR+\angle PRQ+\angle QPR=180$ (Angles of a triangle)
$70+75+\angle QPR=180$
$\angle QPR={35}^{\circ }$