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Two lines AB and CD intersects three parallel lines as shown below. If ∠APQ + ∠ARS + ∠ATU = 300° and ∠DUT + ∠DSR + ∠DQP = 210°, find the angle of intersection of the two lines AB and CD.

Two lines AB and CD intersects three parallel lines as shown below. If ∠APQ + ∠ARS + ∠ATU = 300° and ∠DUT + ∠DSR + ∠DQP = 210°, find the angle of intersection of the two lines AB and CD. Correct Answer 30°

As we know, when a line intersects two or more parallel lines are corresponding intersecting angles are equal,

⇒ ∠APQ = ∠ARS = ∠ATU = 300°/3 = 100°

Similarly,

⇒ ∠DUT = ∠DSR = ∠DQP = 210°/3 = 70°

Now, if the two lines AB and CD intersect at point O, then in ΔTOU,

[ alt="F1 V.G D.K 10.08.2019 D3" src="//storage.googleapis.com/tb-img/production/19/08/F1_V.G_D.K_10.08.2019_D3.png" style="width: 203px; height: 229px;">

⇒ ∠OTU = 180°– 100° = 80°

⇒ ∠OUT = ∠DUT = 70°

But,

⇒ ∠OUT + ∠OTU + ∠TOU = 180°

⇒ 70° + 80° + ∠TOU = 180°

⇒ ∠TOU = 180°– 150° = 30°

∴ Angle of intersection of two lines = 30°

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