Question

A transversal intersects two parallel lines such that the interior angles formed on the same side of it are in the ratio 2:3. What is the difference between the two angles? (A) 36° B) 720 © 108° D) 144°​

Answer 1

$\sf \underline{ \underline{Question : }}$

A transversal intersects two parallel lines such that the interior angles formed on the same side of it are in the ratio 2:3. What is the difference between the two angles? (A) 36° B) 720° C) 108° D) 144°

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$\sf \underline{ \underline{Given : }}$

• A transversal intersects two parallel lines.
• The interior angles formed are in the ratio 2:3

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$\sf \underline{ \underline{To \: Find : }}$

• Difference between the two lines

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$\sf \underline{ \underline{Solution : }}$

~ Let Us Assume :

• ➳ Let one of the angles be = 2x
• ➳ Let the other angle be = 3x

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~ Concept Used :

As sum of interior angles on same side of transversal, intersecting two parallel line is 180°.

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~ Calculating the x :

$\sf{{ \: \: \: \: \: \: \: \: \: \: \: \: \: ⟼\: \: \: \: \: \: 2x \: + \: 3x = 180° }{ \: }}$

$\sf{{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ⟼ \: \: \: \: \: 5x = 180° }{ \: }}$

$\sf{{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ⟼ \: \: \: \: \: \: x = \frac{180°}{5} }{ \: }}$

$\sf{{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ⟼\: \: \: \: \: \: \: x = 36° }{ \: }}$

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~ Finding the two angles :

$\sf{{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ⟼ \: \: \: \: }{ \: 2x = 2 \times 36 = 72°}}$

$\sf{{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ⟼ \: \: \: \: }{ \: 3x = 3 \times 36 = 108°}}$

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~ Calculating the difference :

$\sf \pink{⇢}\small{\underline{{\boxed{\sf{\red{ Difference = Greater \: angle - smaller \: angle }}}}}}$

$\sf \pink{{ \: \: \: \: \: \: \: \: \: \: \: ⟼\: \: \: \: \: } \green{ \: 108° - 72°}}$

$\sf \pink{{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ⟼\: \: \: \: \: \: } \green{ \: 36°}}$

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~ Therefore :

The difference between the two angles is (A) 36°.

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Answer 2

Answer:

Let the angle be 2x and 3x

Sum of angles on the same side of transversal intersecting two parallel lines is 180∘

$2x + 3x = 180 \degree \\ 5x = 180\degree \\ x = 36\degree \\ so \: the \: angles \: are \\ 2x = 2 \times 36\degree = 72\degree \\ 3x = 3 \times 36\degree = 108\degree$

so the smaller angle is 72°