Question

in fig.6.39, sides QP and RQ of /\ PQR are produced to points S and T respectively. if /_PQT=110°, Find /_PRQ.
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Answer 1

Given :

• ∠SPR = 135°
• ∠PQT = 110°

To Find :

• ∠PRQ

Solution :

$\longmapsto\tt{\angle{PQT}+\angle{PQR}=180\degree}$

$\longmapsto\tt{110\degree+\angle{PQR}=180\degree}$

$\longmapsto\tt{\angle{PQR}=180\degree-110\degree}$

$\longmapsto\tt\bold{\angle{PQR}=70\degree}$

Now :

$\longmapsto\tt{\angle{SPR}=\angle{PQR}+\angle{PRQ}\:(Exterior\:angle)}$

$\longmapsto\tt{135\degree=70\degree+\angle{PQR}}$

$\longmapsto\tt{135\degree-70\degree=\angle{PQR}}$

$\longmapsto\tt\bold{\angle{PQR}=65\degree}$

Therefore :

$\longmapsto\tt{\angle{PQR}=70\degree}$

$\longmapsto\tt{\angle{PQR}=65\degree}$