Question

Two lines PQ and RS intersect at O. If ZPOR = 50°, then value of ZROQ is​

Answer 1

Diagram :-

$\setlength{\unitlength}{2mm}\begin{picture}(0,0)\thicklines\put(0,0){\line(3,2){2cm}}\put(10,0){\line(-3,2){2cm}}\put(-1,-1){\sf\footnotesize P}\put(10,7){\sf\footnotesize Q} \put(-1,7){\sf\footnotesize R}\put(10,-1.2){\sf\footnotesize S}\qbezier(3.5,2.5)(2,3)(3.4,4.5)\put(4.4,1.8){\sf\footnotesize O}\put(0,3){ \sf\tiny 50^\circ }\end{picture}$

Solution :-

By observing the given figure,

• ∠POR and ∠QOS are opposite angles

• ∠ROQ and ∠POS are opposite angles

As we know that ,

Opposite angles are always equal .

So here ,

∠POR = 50° = ∠QOS

∠ROQ = ∠POS

And here , adjacent angles sum are always equal to 180°

So here ,

$\leadsto$ ∠ROQ + ∠QOS = 180°

$\leadsto$ ∠ROQ + 50° = 180°

$\leadsto$ ∠ROQ = 180° - 50°

$\leadsto$ ∠ROQ = 130°

Hence , ∠ROQ = 180°