Question

5. In Fig. 6.17, POQ is a line. Ray OR is perpendicular
to line PQ. OS is another ray lying between rays
OP and OR. Prove that
1
ROS
(Z QOS-Z POS).
2​

Answer 1

✯✯ QUESTION ✯✯

POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that angle ROS = 1/2 (angleQOS-anglePOS)..

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✰✰ ANSWER ✰✰

(Refer to the Attachment)

➮Given : -

$\longmapsto\tt{\angle{ROS}=90\degree}$

➮To Prove : -

$\longmapsto\tt{\angle{ROS}=\dfrac{1}{2}(\angle{QOS}-\angle{POS})}$

➮Proof : -

→As POQ is a line :

$\longmapsto\tt{\angle{POS}+\angle{ROS}+\angle{ROQ}=180\degree}$

(Angles made on one side of line)

$\longmapsto\tt{\angle{POS}+\angle{ROS}+90\degree=180\degree}$

$\longmapsto\tt{\angle{POS}+\angle{ROS}=180-90}$

$\longmapsto\tt{\angle{POS}+\angle{ROS}=90\degree}$ -----(1)

➥Also ,

$\longmapsto\tt{\angle{QOS}=\angle{ROS}+\angle{ROQ}}$

$\longmapsto\tt{\angle{QOS}=\angle{ROS}+90\degree}$

$\longmapsto\tt{\angle{QOS}-\angle{ROS}=90\degree}$ -----(2)

➥By Equation 1 and 2 : -

$\longmapsto\tt{\angle{POS}+\angle{ROS}=\angle{QOS}-\angle{ROS}}$

$\longmapsto\tt{\angle{ROS}+\angle{ROS}=\angle{QOS}-\angle{POS}}$

$\longmapsto\tt{\angle{ROS}=\dfrac{1}{2}(\angle{QOS}-\angle{POS})}$

✺ HENCE VERIFIED ✺

Answer 2

Answer:

Step-by-step explanation: