Question

If two exterior angles on the same side of a transversal intersecting two parallel lines are in ratio of 2:3. Then find the larger angle.

Answer 1

Given that, two exterior angles on the same side of a transversal intersecting two ∥ lines are in the ratio of 2: 3.

Need to find: The Larger angle?

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❍ Let's Consider that, the two angles are 2x and 3x respectively.

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$\underline{\pmb{\bf{\dag\;}\frak{As\;we\;know\;that\;:}}}$

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• Sum of exterior angles on the same side of a transversal intersecting two ∥ lines is equal to 180°.

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Therefore,

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$:\implies\sf{2x+3x=180\degree}\\\\\\:\implies\sf{5x=180\degree}\\\\\\:\implies\sf{x=\cancel\dfrac{180}{5}}\\\\\\:\implies\underline{\boxed{\frak{\pmb{\pink{x=36\degree}}}}}\;\bigstar$

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Hence,

• First angle = 2x = 2(36) = 72°
• Second angle = 3x = 3(36) = 108°

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$\therefore\;{\underline{\textsf{Hence,\;the\;measure\;of\;larger\;angle\;is\;{\textbf{108\degree}}.}}}$⠀⠀⠀

Answer 2

Given : Two co interior angles on the same side of a transversal interacting two ||'s lines are in the ratio of 2:3.

To Find : Find the two angles ?

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Solution : Let the first angle be 2x and second angle be 3x.

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$\underline{\frak{As~we~know~that~ :}}$

• $\boxed{\sf\pink{Some~side~of~transversal~is~180^\circ}}$★

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$\pmb{\sf{\underline{According ~to ~the ~Given ~Question~:}}}$

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$\qquad{\sf:\implies{2x ~+ ~3x = ~180^\circ }}$

$\qquad{\sf:\implies{5x ~= ~180^\circ}}$

$\qquad{\sf:\implies{x ~= ~\cancel\dfrac{180^\circ}{5}}}$

$\qquad:\implies{\underline{\boxed{\frak{\pink{\pmb{x = 36^\circ}}}}}}$★

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Therefore,

• First angle, 2x = 2(36) => 72°
• Second angle, 3x = 3(36) => 108°

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Hence,

$\therefore\underline{\sf{The\;angles\;are\; \bf{\underline{\pmb{72^\circ\;\&\;108^\circ}}}}}$

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V E R I F I C A T I O N :

$\qquad{\rm\dashrightarrow{2x~+~3x~=~180^\circ}}$

• Put x = 36°

$\qquad{\rm\dashrightarrow{2 × 36~+~3 × 36~=~180^\circ}}$

$\qquad{\rm\dashrightarrow{72^\circ~+~102^\circ~=~180^\circ}}$

$\qquad\dashrightarrow\large\pmb{\frak\red{180^\circ~=~180^\circ}}$