Question

The diagonals of a rectangle PQRS onterset each other at O. If <POS = 40 degree, find <ROQ and <ORQ.

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Answer 1

Answer:

angle ROQ= 40°

angle ORQ= 70°

Step-by-step explanation:

angle POS= angle ROQ (vertically opposite angles)

angle ROQ= 40°

In triangle ️ RQO:

angle OQR + angle ORQ + 40°= 180° (sum of angles of a ️are 180°)

angle OQR = angle ORQ = x

(because the diagonals of a rectangle are equal and bisecte each other, so OQ=OR, then angle OQR = angle ORQ)

2x+40=180°

2x=140°

x=70°

Hence angle ROQ=40°

angle ORQ=70°

Answer 2

Given :-

<POS = 40°

According to the fig.

<POS = <ROQ [vertically opposite angle]

$\small{ \sf{ \therefore{ < ROQ \: = {40}^{o} }}}$

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