Question

In figure 5, sides QP and RQ of ∆PQR are produced to the points S and T respectively. If ∠SPR= 135 0 and ∠PQT = 110 0 , then find ∠PRQ.​

Answer 1

Answer:

Given :

• ∠SPR = 135°
• ∠PQT =110°

To Find :

• ∠PRQ

Solution :

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

${\longmapsto\tt110\degree+\angle{PQR}=180\degree}$

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

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

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

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

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

$\longmapsto\tt\bold{\angle{PRQ}=65\degree}:$

$\sf \: So , \: \: \red{ \bold{∠PRQ = 65°..}}$