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(A) When a transversal intersects two parallel lines,the sum of the interior angles on the same side of the transversal is $180^{\circ}$ (consecutive

Vedclass · Accepted Answer

$108$

Vedclass · Answer

(A) When a transversal intersects two parallel lines,the sum of the interior angles on the same side of the transversal is $180^{\circ}$ (consecutive interior angles are supplementary).Let the two angles be $2x$ and $3x$.According to the property,$2x + 3x = 180^{\circ}$.$5x = 180^{\circ}$.$x = 180^{\circ} / 5 = 36^{\circ}$.The two angles are $2(36^{\circ}) = 72^{\circ}$ and $3(36^{\circ}) = 108^{\circ}$.The greater of the two angles is $108^{\circ}$.

If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio $2:3,$ then the greater of the two angles is (in $^{\circ}$)

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