Question

7. If two cointerior angles, on the same side of a transversal intersecting two parallel lines,

are in the ratio 2:3, find the angles.​

Answer 1

Answer:

Let the unknown value be x

Angles = 2x , 3x

2x + 3x = 180 (Since, Co-interior angles are supplementary)

5x = 180

x = 180/5

x = 36

angles are 72 and 108 degrees

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.

Need to find: The two angles.

❍ Let the first angle be 2x and second angle be 3x respectively.

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$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}$⠀⠀⠀⠀

⠀

• Sum of Interior angles on the same side of a transversal intersecting two ||'s lines is 180°.

⠀

Therefore,

⠀

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

⠀

Hence,

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

⠀

$\therefore{\underline{\sf{Hence,\; required\;angles\;are\; \bf{72^\circ\;\&\;108^\circ}.}}}$

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