Question

In fig., if PQ।। ST, /_POR=110* and/_RST=130*, find /_QRS.​

Answer 1

hope it will help you mate

Answer 2

✰✰ ANSWER ✰✰

➮Given : -

• $\implies\tt{\angle{PQR}=110\degree}$
• $\implies\tt{\angle{RST}=130\degree}$

➮To Find : -

• $\implies\tt{\angle{QRS}=?}$

★Draw a line XRY // PQ and ST...

(Refer to the Attachment)

$\implies\tt{\angle{PQR}+\angle{QRX}=180\degree}$

$\implies\tt{110\degree+\angle{QRX}=180\degree}$

$\implies\tt{\angle{QRX}=180\degree-110\degree}$

$\implies\tt{\angle{QRX}=70\degree}$

➥Now ,

$\implies\tt{\angle{TSR}+\angle{SRY}=180\degree(Coint.\:Angles)}$

$\implies\tt{130\degree+\angle{SRY}=180\degree}$

$\implies\tt{\angle{SRY}=180\degree-140\degree}$

$\implies\tt{\angle{SRY}=50\degree}$

➥Then ,

$\implies\tt{\angle{QRX}+\angle{QRS}+\angle{SRY}=180\degree}$......(Angles made on one side of line)

$\implies\tt{\angle{QRS}=180\degree-70\degree-50\degree}$

$\implies\tt{\angle{QRS}=60\degree}$