Question

who solved this question I will mark them as brain list​

Answer 1

Step-by-step explanation:

${\LARGE{\mathfrak{\underline{\red{Given :→}}}}}$

${\bold{\sf{OR \: \: ⊥ \: \: PQ}}}$

${\bold{\sf{∠POR \: \: = \: \: 90°}}}$

${\LARGE{\mathfrak{\underline{\red{To \: prove :→}}}}}$

${\bold{\sf{∠ROS \: = \: \frac{1}{2} (∠QOS \: - \: ∠SOP)}}}$

${\LARGE{\mathfrak{\underline{\red{Solution :→}}}}}$

If ∠POR = 90°

Therefore, ∠POS + ∠SOR = 90°

${\bold{\sf{: \: ⟹ \: \: \: \: \: ∠ROS \: = \: 90° \: - \: ∠POS}{\pink{ \: \: ------- \: Equation \: 1}}}}$

∠QOR = 90° (As OR ⊥ PQ)

∠QOS - ∠ROS = 90°

${\bold{\sf{: \: ⟹ \: \: \: \: \: ∠ROS \: = \: ∠QOS \: - \: 90° }{\pink{ \: ------- \: Equation \: 2}}}}$

On Adding Equation 1 and 2 we get,

${\bold{\sf{: \: ⟹ \: \: \: \: \: 2 \: ∠ROS \: = \: ∠OQS \: - \: ∠POS}}}$

${\bold{\sf{: \: ⟹ \: \: \: \: \: ∠ROS \: = \: \frac{1}{2} \: ∠OQS \: - \: ∠POS}}}$

$\\ {\large{\bf{\fbox{\green{Hence Prove}}}}}$