Question

Figure 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 angle ROS = 1/2 ( QOS - POS

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Answer 1

$\huge\mathfrak\pink{Answer}$

POQ= line

QR perpendicular POQ

<ROQ = 90°

★ To prove

<ROS = $\frac{1}{2}$ ( <QOS - <POS)

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎= <PQR = 90° => <POR = 180° - 90° = 90°

<QOS = <ROQ + <ROS

<QOS = 90° + <ROS - - - - (1)

<POS => <POR - <ROS

<POS = 90° - <ROS - - - - (2)

★ Subtracting Equation 1 &

2

<QOS - <POS = 90° + <ROS - (90 - <ROS)

90+ <ROS - 90 + <ROS

‎ ‎‎. $\frac{2}{1}$<ROS

<QOS - <POS

$\frac{1}{2}$ <QOS - <POS = <ROS

‏‏‎ ‎ hence proved ★

Hope it's helps you ☻