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Two Unequal Angles of a Parallelogram Are in the Ratio 2 : 3. Find All Its Angles in Degrees . - Mathematics

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Two unequal angles of a parallelogram are in the ratio 2 : 3. Find all its angles in degrees .

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Solution

Let `∠`A = 2x and `∠`B = 3x

Now,

`∠`A + `∠`B = 180°                           [Co-interior angles are supplementary]

2x + 3x -180°                              [ AD || BC and AB is the transversal]

⇒ 5x =180°

⇒ x = `(180°)/ 5` = 36°

∴`∠`A = 2 ´ 36° = 72°

`∠` B = 3´ 36° = 108°

Now,

`∠`A = `∠`C = 72°                           [Opposite side angles of a parallelogram are equal]

`∠`B = `∠`D =108°

Concept: Pairs of Angles
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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 10 Lines and Angles
Exercise 10.4 | Q 7 | Page 47

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