Name the interior adjacent angles at point Rin
the given figure.
Р
Q
RS
ZPRS
1
ZPRO
2.
ZQPR
3
ZPRS
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(i) PQ Bisects AB at R.
∠PRA and ∠ARS are on straight line PQ.
∴ ∠PRA + ∠ARS = 180° Adjacent angles
50 + ∠ARS = 180°
∠ARS = 180 – 50
∴ x = ∠ARS = 130° (i)
(ii) Similarly, PQ straight line intersects straight line CD at S.
∴∠CSQ = ∠RSD . Vertically opposite angles
∴y = ∠RSD = 130° (ii)
From (i) and (ii),
∠ARS = ∠RYD
x = y = 130°
(iii) Therse are mutual alternate angles
∴x = y = 130°
∴AB || CD.
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